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This worksheet covers Graphing Circles, which is part of the Circle Measurements and Graphs module in the SAT Math course. Practice problems are designed to strengthen key concepts and build confidence.
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View Destroyer Course →Circle Measurements and Graphs • SAT Math
Set 4 — Mastery
What is the standard form of the equation of a circle with center at (3, -2) and a radius of 5?
(x - 3)^{2} + (y + 2)^{2} = 25
(x + 3)^{2} + (y - 2)^{2} = 25
(x - 3)^{2} + (y - 2)^{2} = 25
(x + 3)^{2} + (y + 2)^{2} = 25
If the circle with equation (x + 4)^{2} + (y - 1)^{2} = 36 is graphed, what are the coordinates of its center?
(-4, 1)
(4, -1)
(1, -4)
(-1, 4)
What is the radius of the circle defined by the equation (x - 2)^{2} + (y + 5)^{2} = 49?
7
14
5
6
What is the equation of a circle with a diameter that has endpoints at (1, 2) and (5, 6)?
(x - 3)^{2} + (y - 4)^{2} = 8
(x - 3)^{2} + (y - 4)^{2} = 4
(x - 3)^{2} + (y - 5)^{2} = 8
(x - 3)^{2} + (y - 2)^{2} = 4
A circle is centered at the origin and passes through the point (3, 4). What is the equation of the circle?
x^{2} + y^{2} = 25
x^{2} + y^{2} = 16
x^{2} + y^{2} = 20
x^{2} + y^{2} = 24
Which of the following points lies on the circle defined by the equation (x - 1)^{2} + (y - 2)^{2} = 10?
(1, 2)
(1, 4)
(4, 2)
(1, 0)
What is the distance between the center and a point on the circle with the equation (x + 2)^{2} + (y - 3)^{2} = 16?
4
8
2
6
Find the equation of the circle that has a center at (0, 0) and passes through the point (5, 12).
x^{2} + y^{2} = 169
x^{2} + y^{2} = 25
x^{2} + y^{2} = 144
x^{2} + y^{2} = 169
A circle has an equation of the form (x - 5)^{2} + (y + 3)^{2} = r^{2}. If the radius is 6, what is the value of r^{2}?
36
12
18
24
Which of the following points does NOT lie on the circle defined by (x - 2)^{2} + (y - 3)^{2} = 9?
(2, 3)
(5, 3)
(2, 0)
(2, 6)
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