# How do you write the standard form equation for the circle whose center is at (-2, 3) and that is tangent to the line 20x - 21y - 42 = 0?

Feb 15, 2017

${\left(x + 2\right)}^{2} + {\left(y - 3\right)}^{2} = {\left(\frac{145}{\sqrt{841}}\right)}^{2}$. See the tangent-inclusive Socratic graph.

#### Explanation:

The length of the perpendicular from the center $\left(- 2. 3\right)$ to the

tangent line 20x-21y-42=0#

$= | 20 \left(- 2\right) - 21 \left(3\right) - 42 \frac{|}{\sqrt{{20}^{2} + {21}^{2}}} = \frac{145}{\sqrt{841}}$

${\left(x + 2\right)}^{2} + {\left(y - 3\right)}^{2} = {\left(\frac{145}{\sqrt{841}}\right)}^{2}$