# How do you write an equation for a circle given endpoints of a diameter at (11,18) and (-13, -19)?

Jun 11, 2017

${\left(x + 1\right)}^{2} + {\left(y + \frac{1}{2}\right)}^{2} = \frac{1945}{4}$

#### Explanation:

$A = \left(11 , 18\right) \mathmr{and} B = \left(- 13 , - 19\right)$

The center is $M = \frac{A + B}{2}$ and the radius is $r = | A B \frac{|}{2}$

$M = \frac{\left(11 - 13 , 18 - 19\right)}{2} = \left(- 1 , - \frac{1}{2}\right)$

$r = \frac{\sqrt{{24}^{2} + {37}^{2}}}{2}$