# What is the standard form of the equation of a circle passing through Center at the point (-3, 1) and tangent to the y-axis?

Jan 7, 2016

${\left(x + 3\right)}^{2} + {\left(y - 1\right)}^{2} = 9$

#### Explanation:

I assume you meant "with center at $\left(- 3 , 1\right)$"

The general form for a circle with center $\left(a , b\right)$ and radius $r$ is
$\textcolor{w h i t e}{\text{XXX}} {\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

If the circle has its center at $\left(- 3 , 1\right)$ and is tangent to the Y-axis then it has a radius of $r = 3$.

Substituting $\left(- 3\right)$ for $a$, $1$ for $b$, and $3$ for $r$ in the general form gives:
$\textcolor{w h i t e}{\text{XXX}} {\left(x - \left(- 3\right)\right)}^{2} + \left(y - 1\right) = {3}^{2}$
which simplifies to the Answer above.

graph{(x+3)^2+(y-1)^2=9 [-8.77, 3.716, -2.08, 4.16]}