# How do you find the equation given points A(-4,3) and B(5,-1) are the endpoints of a diameter in circle?

Sep 5, 2016

$\therefore {x}^{2} + {y}^{2} - x - 2 y - 23 = 0$.

#### Explanation:

If $A \left({x}_{1} , {y}_{1}\right) \mathmr{and} B \left({x}_{2} , {y}_{2}\right)$ are the end-points of a diameter of a

circle, then, its eqn. is :

$\left(x - {x}_{1}\right) \left(x - {x}_{2}\right) + \left(y - {y}_{1}\right) \left(y - {y}_{2}\right) = 0$.

Accordingly, the reqd. eqn. is,

$\left(x + 4\right) \left(x - 5\right) + \left(y + 1\right) \left(y - 3\right) = 0$

$\therefore {x}^{2} + {y}^{2} - x - 2 y - 23 = 0$.