# How do you write an equation for a circle with center (2,-6); tangent to the y-axis?

Nov 26, 2017

The equation is: ${\left(x - 2\right)}^{2} + {\left(y + 6\right)}^{2} = 4$

#### Explanation:

The equation of a circle with center $\left(h , k\right)$ and radius $r$ is:

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

We know the center is $\left(2 , - 6\right)$.

Since the circle is tangent to the y-axis, we know that the distance from the center to the y-axis is 2 units, so the radius is 2.

The equation is: ${\left(x - 2\right)}^{2} + {\left(y + 6\right)}^{2} = 4$

Here's a figure:
graph{(x-2)^2+(y+6)^2=4 [-9.13, 10.87, -9.36, 0.64]}