# A circle is centered at C(-5,4) and has a radius of 2, how do you find the equation of a concentric circle with half the radius?

Nov 10, 2015

${\left(x + 5\right)}^{2} + {\left(y - 4\right)}^{2} = 1$

#### Explanation:

A general circle centred at $\left(a , b\right)$ and having radius $r$ has equation ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$.

Hence the given circle has equation ${\left(x + 5\right)}^{2} + {\left(y - 4\right)}^{2} = 4$.

By concentric circle I assume you mean a circle with the same centre point $\left(- 5 , 4\right)$. Thus only the radius is different and is 1 unit.

Therefore the new equation will be ${\left(x + 5\right)}^{2} + {\left(y - 4\right)}^{2} = 1$