How do you find the center (h,k) and radius r of the circle with the given equation 2(x-2)^2+2(y+5)^2=28?

Jan 14, 2016

Rearrange slightly into standard form and read off $\left(h , k\right) = \left(2 , - 5\right)$ and $r = \sqrt{14}$

Explanation:

If you divide both sides by $2$, tweak the monomial in $y$ a bit and express the right hand side as a square you get the following:

${\left(x - 2\right)}^{2} + {\left(y - \left(- 5\right)\right)}^{2} = {\left(\sqrt{14}\right)}^{2}$

This is in the form:

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

with $\left(h , k\right) = \left(2 , - 5\right)$ and $r = \sqrt{14}$