# What is the standard form of the equation of a circle with r = 5; (h, k) = (-5, 2)?

Dec 9, 2015

#### Answer:

${\left(x + 5\right)}^{2} + {\left(y - 2\right)}^{2} = 25$

#### Explanation:

The standard form of the equation of a circle of radius $r$ centered at the point $\left(h , k\right)$ is ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$.

This equation is reflecting the fact that such a circle consists of all points in the plane that are distance $r$ from $\left(h , k\right)$. If a point $P$ has rectangular coordinates $\left(x , y\right)$, then the distance between $P$ and $\left(h , k\right)$ is given by the distance formula $\sqrt{{\left(x - h\right)}^{2} + {\left(y - k\right)}^{2}}$ (which itself comes from the Pythagorean Theorem).

Setting that equal to $r$ and squaring both sides gives the equation ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$.