# How do you write an equation for a circle given endpoints of a diameter at (-5,2) and (3,6)?

##### 1 Answer

Oct 24, 2016

#### Explanation:

First, we have to find the centre of the circle.

This will be halfway between the two endpoints

giving us the point

now we need to find the radius,

take the middle and an end point and find the distance,

giving us

now if we use trigonometry to find the radius

now the equation of a circle is,

where a and b are the coordinates of the centre.

sub in,

giving us,

for the equation of our circle.