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Circle Equations

This worksheet covers Circle Equations, which is part of the Circles Destroyer module in the SAT Math Destroyer Crash Course course. Practice problems are designed to strengthen key concepts and build confidence.

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Circle Equations

Circles Destroyer • SAT Math Destroyer Crash Course

Set 3 — Mastery

What is the equation of a circle with center at $(2, -3)$ and a radius of $5$ ?

A) $(x - 2)^{2} + (y + 3)^{2} = 25$

B) $(x + 2)^{2} + (y - 3)^{2} = 25$

C) $(x - 2)^{2} + (y - 3)^{2} = 5$

D) $(x + 2)^{2} + (y + 3)^{2} = 5$

A circle has the equation $(x + 4)^{2} + (y - 1)^{2} = 36$ . What is the radius of the circle?

A) $6$

B) $4$

C) $5$

D) $3$

If the center of a circle is at the origin and its radius is $r$ , which of the following is the correct equation of the circle?

A) $x^{2} + y^{2} = r^{2}$

B) $x^{2} + y^{2} = r$

C) $x + y = r^{2}$

D) $x^{2} + y^{2} = 2r$

A circle is described by the equation $x^{2} + y^{2} - 4x + 6y + 9 = 0$ . What are the coordinates of the center of the circle?

A) $(2, -3)$

B) $(-2, 3)$

C) $(2, 3)$

D) $(-2, -3)$

What is the equation of a circle with a diameter that has endpoints at $(1, 2)$ and $(7, 8)$ ?

A) $(x - 4)^{2} + (y - 5)^{2} = 18$

B) $(x - 4)^{2} + (y - 5)^{2} = 20$

C) $(x - 4)^{2} + (y - 5)^{2} = 10$

D) $(x - 4)^{2} + (y - 5)^{2} = 16$

Given the circle $(x - 3)^{2} + (y + 2)^{2} = 16$ , what is the area of the circle?

A) $16 ext{π}$

B) $8 ext{π}$

C) $4 ext{π}$

D) $32 ext{π}$

A circle is tangent to the x-axis at the point $(5, 0)$ . If the radius is $3$ , what is the equation of the circle?

A) $(x - 5)^{2} + (y - 3)^{2} = 9$

B) $(x - 5)^{2} + (y + 3)^{2} = 9$

C) $(x + 5)^{2} + (y - 3)^{2} = 9$

D) $(x + 5)^{2} + (y + 3)^{2} = 9$

What is the standard form of the equation for a circle whose center is at $(-1, 4)$ and passes through the point $(1, 4)$ ?

A) $(x + 1)^{2} + (y - 4)^{2} = 4$

B) $(x + 1)^{2} + (y - 4)^{2} = 16$

C) $(x + 1)^{2} + (y - 4)^{2} = 8$

D) $(x + 1)^{2} + (y - 4)^{2} = 2$

For the equation of a circle $(x - 4)^{2} + (y + 1)^{2} = 25$ , which point lies outside the circle?

A) $(4, -1)$

B) $(8, -1)$

C) $(2, -1)$

D) $(4, 1)$

10.

What is the distance between the centers of the circles given by the equations $(x - 1)^{2} + (y - 2)^{2} = 9$ and $(x + 3)^{2} + (y + 2)^{2} = 4$ ?

A) $4$

B) $5$

C) $6$

D) $8$

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