Precalculus Examples

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

Step 1

This is the form of a circle. Use this form to determine the center and radius of the circle.

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

Step 2

Match the values in this circle to those of the standard form. The variable $r$ represents the radius of the circle, $h$ represents the x-offset from the origin, and $k$ represents the y-offset from origin.

$r = 3$

$h = 2$

$k = - 3$

Step 3

The center of the circle is found at $(h, k)$ .

Center: $(2, - 3)$

Step 4

These values represent the important values for graphing and analyzing a circle.

Center: $(2, - 3)$

Radius: $3$

Step 5