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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 2 — Mastery

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

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

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

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

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

A circle has the equation $x^{2} + y^{2} - 4x + 6y - 12 = 0$ . What is the center of the circle?

$(2, -3)$

$(2, 3)$

$(-2, -3)$

$(-2, 3)$

If a circle's diameter is $10$ , what is its area?

$25$

$100 rac{ ext{π}}{4}$

$25 ext{π}$

$50 ext{π}$

A circle is centered at the origin and passes through the point $(4, 3)$ . What is the radius of the circle?

$5$

$7$

$4$

$3$

Which of the following points lies outside the circle given by the equation $(x - 1)^{2} + (y - 2)^{2} = 16$ ?

$(5, 2)$

$(1, 6)$

$(1, -2)$

$(0, 0)$

What is the equation of a circle with a center at $(-1, 1)$ and passing through the point $(1, 1)$ ?

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

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

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

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

The equation of a circle is given as $x^{2} + y^{2} + 2x - 4y - 3 = 0$ . What is the radius of this circle?

$3$

$rac{5}{2}$

$rac{7}{2}$

$rac{9}{2}$

If a circle has the equation $(x - 5)^{2} + (y + 3)^{2} = 36$ , what is the distance from the center to the point $(5, 0)$ ?

$3$

$6$

$9$

$12$

Which equation represents a circle that is tangent to the x-axis at the point $(1, 0)$ ?

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

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

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

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

10.

What is the length of the diameter of a circle whose equation is $(x + 4)^{2} + (y - 2)^{2} = 36$ ?

$6$

$12$

$18$

$24$

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