# How do you write the general form of a circle given center is (4,-6) and tangent to line x=-1?

Jan 15, 2016

#### Answer:

${\left(x - 4\right)}^{2} + {\left(y + 6\right)}^{2} = 25$

#### Explanation:

The general form of a circle is ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$ where $\left(h , k\right)$ is the center of the circle and $r$ is the radius.

the radius can be calculated as the distance from the center to the tangent line, which is given by the difference in their x-coordinates.
$r = 4 - \left(- 1\right) = 5$

The general equation is therefore

${\left(x - 4\right)}^{2} + {\left(y + 6\right)}^{2} = 25$