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Graphing Circles

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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Graphing Circles

Circle Measurements and Graphs • SAT Math

Set 1 — Foundation

What is the center of the circle given by the equation $(x - 3)^{2} + (y + 2)^{2} = 16$ ?

(3, -2)

(-3, 2)

(2, 3)

(3, 2)

What is the radius of the circle represented by the equation $(x + 1)^{2} + (y - 4)^{2} = 25$ ?

Which of the following points lies on the circle defined by $(x - 1)^{2} + (y - 3)^{2} = 9$ ?

(4, 3)

(1, 6)

(1, 2)

(0, 3)

Identify the standard form of the equation for a circle with center $(0, 0)$ and radius $3$ .

$x^{2} + y^{2} = 9$

$x^{2} + y^{2} = 3$

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

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

What is the equation of a circle with center $(2, -1)$ and radius $4$ ?

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

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

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

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

Which equation represents a circle centered at $(5, 5)$ with a radius of $2$ ?

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

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

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

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

What is the diameter of a circle whose equation is $(x - 1)^{2} + (y + 2)^{2} = 36$ ?

What is the relationship between the radius and diameter of a circle?

Diameter = Radius × 2

Diameter = Radius ÷ 2

Diameter = 2 × Radius^{2}

Diameter = Radius + 2

If a circle has a radius of $r$ , what is its area?

$\pi r^{2}$

$2\pi r$

$r^{2} \pi^{2}$

$\frac{1}{2}\pi r^{2}$

10.

Which of the following is NOT a characteristic of a circle?

All points are equidistant from the center.

The diameter is the longest chord.

A circle has corners.

The radius is half the diameter.

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