Question

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`?

Answer 1

Rearrange slightly into standard form and read off `(h, k) = (2, -5)` 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:

`(x-2)^2+(y-(-5))^2 = (sqrt(14))^2`

This is in the form:

`(x-h)^2+(y-k)^2=r^2`

with `(h, k) = (2, -5)` and `r = sqrt(14)`