Precalculus Examples

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

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.

$r = 4$

$h = - 2$

$k = - 1$

Step 3

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

Center: $(- 2, - 1)$

Step 4

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

Center: $(- 2, - 1)$

Radius: $4$

Step 5