Question

Graph the circle with center at (3, -2), which also passes through the point (0, 2). Label the center and at least four points on the circle. Write the equation of the circle.

Answer 1

so -> http://www.mathwarehouse.com/geometry/circle/images/equation-of-circle/general-formula-equation-of-circle.png

^ as you can see
we have the center of the circle, that is, ( 3, -2 )
however we do not have the radius
but we know the circle passes through (0, 2)



so to find the radius, just use the distance formula :) that is
\(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 3}}\quad ,&{\color{blue}{ -2}})\quad &({\color{red}{ 0}}\quad ,&{\color{blue}{ 2}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 2

once you have the radius, the center is given, plug them in the circle equation