Quick Answer
SAT circle equations practice questions test standard form, center and radius, point testing, writing equations, transformations, completing the square, tangency, and intersections.
What Should You Know?
- Standard form is (x-h)²+(y-k)²=r².
- The center is (h,k).
- The right side is radius squared.
- Use substitution to test points.
- Use distance to find radius.
- Complete both squares in expanded equations.
- A tangent line is one radius from the center.
In This Guide
Start With SAT Math Topic-Wise Practice
Connect circle-equation practice with weekly score planning.
Download the SAT Prep Guide E-Book
Organize circle-equation and coordinate-geometry practice with a clear weekly plan.
Download SAT Prep Guide E-BookWhat Does the SAT Test in Circle Equation Questions?
Students may need to identify center and radius, write an equation, test a point, complete the square, or analyze tangent and intersection conditions.
| Skill Area | What It Tests | Questions |
|---|---|---|
| Standard form | Center, radius, area, circumference | Q1-Q15 |
| Points and equations | Substitution, distance, equation writing | Q16-Q30 |
| Expanded form | Translations, reflections, completing square | Q31-Q45 |
| Advanced | Tangency, intersections, mixed models | Q46-Q70 |
Download Free SAT Study Resources For U.S. Students
To begin your preparation with organized practice, download our free SAT Prep E-Book, SAT Math Question Bank, and SAT English Question Bank. These tools are intended to assist students in comprehending the style of the Digital SAT, increasing their accuracy, and boosting their self-assurance prior to test day.
How Is Standard Form Tested?
Identify center, radius, diameter, area, circumference, and equations.
STANDARD FORMEASYQuestion 1
For the circle (x-3)²+(y+2)²=25, what is the center?
Which choice is correct?
A) (-3,2)
B) (3,-2)
C) (3,2)
D) (-3,-2)
Show full solution
Correct answer: B) (3,-2)
The center is (3,-2).
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMEASYQuestion 2
For the circle (x-3)²+(y+2)²=25, what is the radius?
Which choice is correct?
A) 5
B) 10
C) 25
D) 50
Show full solution
Correct answer: A) 5
Since r²=25, r=5.
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMEASYQuestion 3
For the circle (x+4)²+(y-7)²=36, what is the center?
Which choice is correct?
A) (4,-7)
B) (-4,7)
C) (-4,-7)
D) (4,7)
Show full solution
Correct answer: B) (-4,7)
The center is (-4,7).
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMEASYQuestion 4
For the circle (x+4)²+(y-7)²=36, what is the radius?
Which choice is correct?
A) 3
B) 6
C) 18
D) 36
Show full solution
Correct answer: B) 6
Since r²=36, r=6.
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMEASYQuestion 5
For the circle x²+y²=81, what is the center?
Which choice is correct?
A) (0,0)
B) (9,0)
C) (0,9)
D) (9,9)
Show full solution
Correct answer: A) (0,0)
The circle is centered at the origin.
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMEASYQuestion 6
For the circle x²+y²=81, what is the radius?
Which choice is correct?
A) 8
B) 9
C) 18
D) 81
Show full solution
Correct answer: B) 9
Since r²=81, r=9.
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMEASYQuestion 7
For the circle (x-5)²+(y+2)²=16, what is the center?
Which choice is correct?
A) (-5,2)
B) (5,-2)
C) (5,2)
D) (-5,-2)
Show full solution
Correct answer: B) (5,-2)
The center is (5,-2).
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMEASYQuestion 8
For the circle (x-5)²+(y+2)²=16, what is the diameter?
Which choice is correct?
A) 4
B) 8
C) 16
D) 32
Show full solution
Correct answer: B) 8
The radius is 4, so the diameter is 8.
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMMEDIUMQuestion 9
For the circle (x+3)²+(y-6)²=49, what is the center?
Which choice is correct?
A) (-3,6)
B) (3,-6)
C) (-3,-6)
D) (3,6)
Show full solution
Correct answer: A) (-3,6)
The center is (-3,6).
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMMEDIUMQuestion 10
For the circle (x+3)²+(y-6)²=49, what is the area?
Which choice is correct?
A) 7π
B) 14π
C) 49π
D) 98π
Show full solution
Correct answer: C) 49π
The radius is 7, so area=49π.
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMMEDIUMQuestion 11
For the circle (x-1)²+(y-5)²=64, what is the diameter?
Which choice is correct?
A) 8
B) 16
C) 32
D) 64
Show full solution
Correct answer: B) 16
The radius is 8, so diameter=16.
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMMEDIUMQuestion 12
For the circle (x-4)²+(y+1)²=100, what is the circumference?
Which choice is correct?
A) 10π
B) 20π
C) 50π
D) 100π
Show full solution
Correct answer: B) 20π
The radius is 10, so circumference=20π.
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMMEDIUMQuestion 13
For the circle (x+8)²+(y+5)²=9, what is the center?
Which choice is correct?
A) (8,5)
B) (-8,-5)
C) (-8,5)
D) (8,-5)
Show full solution
Correct answer: B) (-8,-5)
The center is (-8,-5).
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMMEDIUMQuestion 14
For the circle (x-h)²+(y-k)²=121, what is the radius?
Which choice is correct?
A) 11
B) 22
C) 60.5
D) 121
Show full solution
Correct answer: A) 11
Since r²=121, r=11.
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
STANDARD FORMMEDIUMQuestion 15
For the circle x²+(y+4)²=25, what is the center?
Which choice is correct?
A) (0,4)
B) (0,-4)
C) (4,0)
D) (-4,0)
Show full solution
Correct answer: B) (0,-4)
The center is (0,-4).
SAT trap: Use (x-h)²+(y-k)²=r² and reverse the signs inside parentheses.
Build Stronger SAT Coordinate Geometry Skills
Connect standard form with graph interpretation.
How Are Points and Circle Equations Tested?
Use substitution and distance to test points and write equations.
POINTS AND EQUATIONSMEDIUMQuestion 16
Does (3,4) lie on x²+y²=25?
Which choice is correct?
A) Yes
B) No
C) Only if x>0
D) Cannot tell
Show full solution
Correct answer: A) Yes
3²+4²=25.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 17
Does (4,4) lie on x²+y²=25?
Which choice is correct?
A) Yes
B) No
C) Only if y>0
D) Cannot tell
Show full solution
Correct answer: B) No
4²+4²=32, not 25.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 18
A circle centered at the origin passes through (5,12). What is its radius?
Which choice is correct?
A) 7
B) 13
C) 17
D) 25
Show full solution
Correct answer: B) 13
√(5²+12²)=13.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 19
A circle centered at (2,3) passes through (8,11). What is its radius?
Which choice is correct?
A) 8
B) 10
C) 12
D) 14
Show full solution
Correct answer: B) 10
√(6²+8²)=10.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 20
Which equation has center (2,3) and passes through (8,11)?
Which choice is correct?
A) (x-2)²+(y-3)²=10
B) (x-2)²+(y-3)²=100
C) (x+2)²+(y+3)²=100
D) (x-8)²+(y-11)²=100
Show full solution
Correct answer: B) (x-2)²+(y-3)²=100
The radius is 10, so r²=100.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 21
Which equation has center (-1,4) and passes through (4,4)?
Which choice is correct?
A) (x+1)²+(y-4)²=25
B) (x-1)²+(y+4)²=25
C) (x+1)²+(y-4)²=5
D) (x-4)²+(y-4)²=25
Show full solution
Correct answer: A) (x+1)²+(y-4)²=25
The radius is 5.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 22
Which point lies on (x-1)²+(y+2)²=25?
Which choice is correct?
A) (6,-2)
B) (1,2)
C) (4,0)
D) (-1,-2)
Show full solution
Correct answer: A) (6,-2)
The point is 5 units from the center (1,-2).
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 23
Which point is inside x²+y²=36?
Which choice is correct?
A) (6,0)
B) (3,4)
C) (0,7)
D) (6,6)
Show full solution
Correct answer: B) (3,4)
3²+4²=25<36.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 24
Which point is outside x²+y²=49?
Which choice is correct?
A) (0,7)
B) (3,4)
C) (6,6)
D) (5,0)
Show full solution
Correct answer: C) (6,6)
6²+6²=72>49.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 25
On (x-2)²+(y-1)²=16, if x=6, what is y?
Which choice is correct?
A) -1
B) 0
C) 1
D) 3
Show full solution
Correct answer: C) 1
16+(y-1)²=16, so y=1.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 26
On x²+y²=100, x=8 and y>0. What is y?
Which choice is correct?
A) 4
B) 6
C) 8
D) 10
Show full solution
Correct answer: B) 6
64+y²=100, so y=6.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 27
A circle centered at (3,-2) has radius √13. Which point lies on it?
Which choice is correct?
A) (5,1)
B) (6,2)
C) (4,2)
D) (1,0)
Show full solution
Correct answer: A) (5,1)
The squared distance is 2²+3²=13.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 28
A circle has center (4,5) and passes through (4,-1). What is its diameter?
Which choice is correct?
A) 6
B) 12
C) 18
D) 36
Show full solution
Correct answer: B) 12
The radius is 6.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 29
A circle centered at (-2,-3) passes through (1,1). What is its area?
Which choice is correct?
A) 5π
B) 10π
C) 25π
D) 50π
Show full solution
Correct answer: C) 25π
The radius is 5, so area=25π.
SAT trap: Substitute coordinates or use the distance formula carefully.
POINTS AND EQUATIONSMEDIUMQuestion 30
A circle centered at (7,0) is tangent to the y-axis. What is its radius?
Which choice is correct?
A) 0
B) 7
C) 14
D) 49
Show full solution
Correct answer: B) 7
The center is 7 units from the y-axis.
SAT trap: Substitute coordinates or use the distance formula carefully.
How Are Transformations and Expanded Forms Tested?
Use translations, reflections, dilations, expansion, and completing the square.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 31
Translate (x-3)²+(y+2)²=16 five units right. What is the new center?
Which choice is correct?
A) (-2,-2)
B) (3,3)
C) (8,-2)
D) (8,2)
Show full solution
Correct answer: C) (8,-2)
The center moves from (3,-2) to (8,-2).
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 32
Translate (x+4)²+(y-1)²=9 three units down. What is the new center?
Which choice is correct?
A) (-4,-2)
B) (-1,1)
C) (-4,4)
D) (4,-2)
Show full solution
Correct answer: A) (-4,-2)
The center moves from (-4,1) to (-4,-2).
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 33
Translate x²+y²=25 two units left and six units up. Which equation results?
Which choice is correct?
A) (x-2)²+(y+6)²=25
B) (x+2)²+(y-6)²=25
C) (x+2)²+(y+6)²=25
D) (x-2)²+(y-6)²=25
Show full solution
Correct answer: B) (x+2)²+(y-6)²=25
The new center is (-2,6).
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 34
What is the center of x²+y²-6x+8y-11=0?
Which choice is correct?
A) (-3,4)
B) (3,-4)
C) (6,-8)
D) (-6,8)
Show full solution
Correct answer: B) (3,-4)
Completing the square gives (x-3)²+(y+4)²=36.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 35
What is the radius of x²+y²-6x+8y-11=0?
Which choice is correct?
A) 3
B) 6
C) 11
D) 36
Show full solution
Correct answer: B) 6
Standard form has r²=36.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 36
What is the center of x²+y²+10x-4y+13=0?
Which choice is correct?
A) (5,-2)
B) (-5,2)
C) (-10,4)
D) (10,-4)
Show full solution
Correct answer: B) (-5,2)
Standard form is (x+5)²+(y-2)²=16.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 37
What is the radius of x²+y²+10x-4y+13=0?
Which choice is correct?
A) 2
B) 4
C) 8
D) 16
Show full solution
Correct answer: B) 4
Standard form has r²=16.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 38
Which expanded equation equals (x-2)²+(y+3)²=25?
Which choice is correct?
A) x²+y²-4x+6y-12=0
B) x²+y²+4x-6y-12=0
C) x²+y²-4x+6y+12=0
D) x²+y²-2x+3y-25=0
Show full solution
Correct answer: A) x²+y²-4x+6y-12=0
Expand and combine constants.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 39
Which standard form matches x²+y²-8x-2y+8=0?
Which choice is correct?
A) (x-4)²+(y-1)²=9
B) (x+4)²+(y+1)²=9
C) (x-4)²+(y-1)²=25
D) (x+4)²+(y+1)²=25
Show full solution
Correct answer: A) (x-4)²+(y-1)²=9
Complete both squares.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 40
Reflect (x-1)²+(y-2)²=9 across the x-axis. What is the new center?
Which choice is correct?
A) (-1,2)
B) (1,-2)
C) (-1,-2)
D) (1,2)
Show full solution
Correct answer: B) (1,-2)
Only the y-coordinate changes sign.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 41
Reflect (x+3)²+(y-5)²=4 across the y-axis. What is the new center?
Which choice is correct?
A) (-3,-5)
B) (3,5)
C) (3,-5)
D) (-3,5)
Show full solution
Correct answer: B) (3,5)
Only the x-coordinate changes sign.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 42
A circle has radius 3. A dilation by factor 2 is centered at its center. What is the new radius?
Which choice is correct?
A) 3
B) 5
C) 6
D) 9
Show full solution
Correct answer: C) 6
The radius doubles.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 43
Dilate x²+y²=16 by factor 3 about the origin. Which equation results?
Which choice is correct?
A) x²+y²=48
B) x²+y²=144
C) x²+y²=256
D) x²+y²=12
Show full solution
Correct answer: B) x²+y²=144
The radius changes from 4 to 12.
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 44
Shift (x-2)²+(y+1)²=36 four left and five down. Which equation results?
Which choice is correct?
A) (x+2)²+(y+6)²=36
B) (x-6)²+(y-4)²=36
C) (x+2)²+(y-4)²=36
D) (x-2)²+(y+6)²=36
Show full solution
Correct answer: A) (x+2)²+(y+6)²=36
The new center is (-2,-6).
SAT trap: Track the center first, then write or simplify the equation.
TRANSFORMATIONS AND EXPANDED FORMHARDQuestion 45
Which circle is congruent to (x-1)²+(y-2)²=49 and centered at (-4,6)?
Which choice is correct?
A) (x+4)²+(y-6)²=49
B) (x-4)²+(y+6)²=49
C) (x+4)²+(y-6)²=7
D) (x-4)²+(y+6)²=7
Show full solution
Correct answer: A) (x+4)²+(y-6)²=49
Congruent circles keep the same radius.
SAT trap: Track the center first, then write or simplify the equation.
Practice More SAT Circle and Coordinate Math
Build accuracy with completing the square and translations.
How Are Tangency and Intersections Tested?
Use distance to axes and substitution to count intersections.
TANGENCY AND INTERSECTIONSHARDQuestion 46
A circle centered at (0,0) is tangent to x=5. What is its equation?
Which choice is correct?
A) x²+y²=5
B) x²+y²=10
C) x²+y²=25
D) (x-5)²+y²=25
Show full solution
Correct answer: C) x²+y²=25
The radius is 5.
SAT trap: Use center-to-line distance and substitution carefully.
TANGENCY AND INTERSECTIONSHARDQuestion 47
A circle centered at (3,4) is tangent to the x-axis. What is its radius?
Which choice is correct?
A) 3
B) 4
C) 5
D) 7
Show full solution
Correct answer: B) 4
Distance to the x-axis is |4|.
SAT trap: Use center-to-line distance and substitution carefully.
TANGENCY AND INTERSECTIONSHARDQuestion 48
A circle centered at (-6,2) is tangent to the y-axis. Which equation is correct?
Which choice is correct?
A) (x+6)²+(y-2)²=36
B) (x-6)²+(y+2)²=36
C) (x+6)²+(y-2)²=6
D) (x-6)²+(y+2)²=6
Show full solution
Correct answer: A) (x+6)²+(y-2)²=36
The radius is 6.
SAT trap: Use center-to-line distance and substitution carefully.
TANGENCY AND INTERSECTIONSHARDQuestion 49
How many intersections do x²+y²=25 and y=0 have?
Which choice is correct?
A) 0
B) 1
C) 2
D) Infinitely many
Show full solution
Correct answer: C) 2
The points are (5,0) and (-5,0).
SAT trap: Use center-to-line distance and substitution carefully.
TANGENCY AND INTERSECTIONSHARDQuestion 50
How many intersections do x²+y²=25 and x=5 have?
Which choice is correct?
A) 0
B) 1
C) 2
D) Infinitely many
Show full solution
Correct answer: B) 1
The line is tangent at (5,0).
SAT trap: Use center-to-line distance and substitution carefully.
TANGENCY AND INTERSECTIONSHARDQuestion 51
How many intersections do x²+y²=25 and x=6 have?
Which choice is correct?
A) 0
B) 1
C) 2
D) Infinitely many
Show full solution
Correct answer: A) 0
The line lies outside the circle.
SAT trap: Use center-to-line distance and substitution carefully.
TANGENCY AND INTERSECTIONSHARDQuestion 52
The circles x²+y²=25 and (x-8)²+y²=9 are externally tangent. What is the center distance?
Which choice is correct?
A) 2
B) 5
C) 8
D) 14
Show full solution
Correct answer: C) 8
The center distance equals 5+3=8.
SAT trap: Use center-to-line distance and substitution carefully.
TANGENCY AND INTERSECTIONSHARDQuestion 53
Two circles have radii 4 and 7 and are internally tangent. What is the center distance?
Which choice is correct?
A) 3
B) 4
C) 7
D) 11
Show full solution
Correct answer: A) 3
The center distance equals 7-4=3.
SAT trap: Use center-to-line distance and substitution carefully.
TANGENCY AND INTERSECTIONSHARDQuestion 54
A chord through the center is called what?
Which choice is correct?
A) Radius
B) Tangent
C) Diameter
D) Secant ray
Show full solution
Correct answer: C) Diameter
A chord through the center is a diameter.
SAT trap: Use center-to-line distance and substitution carefully.
TANGENCY AND INTERSECTIONSHARDQuestion 55
A circle has center (1,2) and radius 5. Which horizontal tangent lies above the center?
Which choice is correct?
A) y=2
B) y=5
C) y=7
D) y=-3
Show full solution
Correct answer: C) y=7
Five units above y=2 is y=7.
SAT trap: Use center-to-line distance and substitution carefully.
What Do Hard Mixed Circle Equation Questions Look Like?
Combine expanded form, missing coordinates, tangency, and scaling.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 56
What is the center of x²+y²-4x+6y-12=0?
Which choice is correct?
A) (-2,3)
B) (2,-3)
C) (4,-6)
D) (-4,6)
Show full solution
Correct answer: B) (2,-3)
Standard form is (x-2)²+(y+3)²=25.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 57
What is the radius of x²+y²-4x+6y-12=0?
Which choice is correct?
A) 3
B) 5
C) 12
D) 25
Show full solution
Correct answer: B) 5
Standard form has r²=25.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 58
A circle has center (a,2), radius 5, and passes through (7,6). If a<7, what is a?
Which choice is correct?
A) 2
B) 3
C) 4
D) 6
Show full solution
Correct answer: C) 4
(7-a)²+4²=25 gives a=4 or 10; choose 4.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 59
(x-2)²+(y+1)²=25 intersects y=-1 at what x-values?
Which choice is correct?
A) -3 and 7
B) -5 and 5
C) 2 only
D) 0 and 4
Show full solution
Correct answer: A) -3 and 7
(x-2)²=25, so x=2±5.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 60
(x+1)²+(y-4)²=16 intersects x=-1 at what y-values?
Which choice is correct?
A) 0 and 8
B) -4 and 4
C) 4 only
D) 1 and 7
Show full solution
Correct answer: A) 0 and 8
(y-4)²=16, so y=4±4.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 61
A circle has center (3,5) and passes through (9,13). Which equation is correct?
Which choice is correct?
A) (x-3)²+(y-5)²=10
B) (x-3)²+(y-5)²=100
C) (x+3)²+(y+5)²=100
D) (x-9)²+(y-13)²=100
Show full solution
Correct answer: B) (x-3)²+(y-5)²=100
The radius is 10.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 62
What is the area of x²+y²+2x-12y+21=0?
Which choice is correct?
A) 4π
B) 8π
C) 16π
D) 32π
Show full solution
Correct answer: C) 16π
Standard form is (x+1)²+(y-6)²=16.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 63
A circle centered at (4,-2) is tangent to the y-axis. What is its circumference?
Which choice is correct?
A) 4π
B) 8π
C) 16π
D) 32π
Show full solution
Correct answer: B) 8π
The radius is 4, so circumference=8π.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 64
On (x-5)²+(y+3)²=64, y=-3 and x<5. What is x?
Which choice is correct?
A) -3
B) 5
C) 13
D) 21
Show full solution
Correct answer: A) -3
x=5±8; choose -3.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
HARD MIXED CIRCLE EQUATIONSHARDQuestion 65
A circle’s radius increases by 20%. By what factor does r² change?
Which choice is correct?
A) 1.2
B) 1.4
C) 1.44
D) 2.4
Show full solution
Correct answer: C) 1.44
1.2²=1.44.
SAT trap: Complete the square or apply the circle condition before selecting an answer.
What Do Student-Produced Responses Look Like?
Enter the requested radius, center coordinate, or intersection value.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 66
What is the radius of (x-4)²+(y+2)²=169?
Enter your answer.
Show full solution
Correct answer: 13
r²=169, so r=13.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 67
What is the x-coordinate of the center of (x+7)²+(y-3)²=25?
Enter your answer.
Show full solution
Correct answer: -7
The center is (-7,3).
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 68
A circle centered at the origin passes through (9,12). What is its radius?
Enter your answer.
Show full solution
Correct answer: 15
√(9²+12²)=15.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 69
For x²+y²-10x+4y-20=0, what is the x-coordinate of the center?
Enter your answer.
Show full solution
Correct answer: 5
The center is (5,-2).
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 70
The circle x²+y²=64 intersects the positive x-axis at what x-value?
Enter your answer.
Show full solution
Correct answer: 8
Set y=0 and take the positive root.
SAT trap: Enter only the requested numerical value.
Common SAT Circle Equation Mistakes
| Mistake | Correction |
|---|---|
| Using center signs directly | Reverse signs inside parentheses |
| Reading r² as r | Take the positive square root |
| Using a point as the center | Use the given center and calculate radius |
| Completing one square only | Complete both x and y squares |
Two-Week Study Plan
| Days | Focus |
|---|---|
| 1-3 | Q1-Q15 |
| 4-7 | Q16-Q30 |
| 8-10 | Q31-Q45 |
| 11-14 | Q46-Q70 and review |
Frequently Asked Questions About SAT Circle Equations Practice Questions
Are circle equations tested on the Digital SAT?
Yes. They may appear in Geometry and Advanced Math questions.
What is the standard form?
(x-h)²+(y-k)²=r².
How do I find the center?
Reverse the signs inside the parentheses.
How do I find the radius?
Take the positive square root of the right side.
How do I test a point?
Substitute its coordinates into the equation.
How do I write an equation from a center and point?
Use distance to find r, then write standard form.
How do I convert expanded form?
Complete the square for x and y.
How many questions should I practice?
Practice standard form, points, transformations, completing square, tangency, and intersections.
Post a Comment