# How do you write an equation of a circle whose diameter has endpoints (-4, 2) and (4, -4)?

Mar 11, 2018

${x}^{2} + {y}^{2} + 2 y = 24$

This is the equation of the circle.

#### Explanation:

The equation of a circle with given end points of Diameter as $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right)$ is $\left(x - {x}_{1}\right) \left(x - {x}_{2}\right) + \left(y - {y}_{1}\right) \left(y - {y}_{2}\right) = 0$

Using this formula we get the equation as :-

$\left(x - \left(- 4\right)\right) \left(x - 4\right) + \left(y - 2\right) \left(y - \left(- 4\right)\right) = 0$

$\Rightarrow \left(x + 4\right) \left(x - 4\right) + \left(y - 2\right) \left(y + 4\right) = 0$

$\Rightarrow {x}^{2} + {y}^{2} + 2 y - 24 = 0$

$\therefore {x}^{2} + {y}^{2} + 2 y = 24$