Precalculus Examples

$6 x^{2} + 6 y^{2} = 144$

Step 1

Divide both sides of the equation by $6$ .

$x^{2} + y^{2} = 24$

Step 2

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 3

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.

$r = 2 \sqrt{6}$

$h = 0$

$k = 0$

Step 4

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

Center: $(0, 0)$

Step 5

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

Center: $(0, 0)$

Radius: $2 \sqrt{6}$

Step 6