How do you find the general form of the equation of a circle with this equation in standard form (-2-h)^2+(3-k)^2=25?

May 16, 2016

Assuming that the intent of the given equation is that $\left(x , y\right) = \left(- 2 , 3\right)$ is a point on the circumference of the circle and $\left(h , k\right)$ is the center
then there is no simple standard form equation.

Explanation:

The intent of this question is not completely clear (at least to me).

I have assumed that what we are given is intended to be of the generalized form:
$\textcolor{w h i t e}{\text{XXX}} {\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$
with given (sample) point for $\left(x , y\right)$ and radius squared ${r}^{2}$
with the objective of finding constants for the center $\left(h , k\right)$

However as can been seen in the image below there are multiple (infinite number) of circles with $\left(x , y\right) = \left(- 2 , 3\right)$ as a point on the circumference and radius of $r = 5$ (i.e. ${r}^{2} = 25$).

The collection of centers for these circles form a circle themselves at a distance of $5$ from the given point $\left(- 2 , 3\right)$