Question

Help .. How do you identify its center and radius?

Answer 1

$x^{2} + (y-3)^{2} =18$

Move all variables to the left side and all constants to the right side.

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

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

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.

$r$= $3\sqrt{2}$

$h$= 0

$k$  = 3

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

Center:  ( 0,3)

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

Center:  ( 0 , 3)

Radius:  $3\sqrt{2}$