# How do you find the general form of the equation of this circle given endpoints of a diameter of the circle are P(-2,5) and Q(4,9)?

Jan 10, 2016

If you know the endpoints of the diameter, then the midpoint is the center of the circle...

#### Explanation:

Center $= \left[\left(\frac{1}{2}\right) \left(- 2 + 4\right) , \left(\frac{1}{2}\right) \left(5 + 9\right)\right] = \left(1 , 7\right) = \left(h , k\right)$

Using the distance formula , now find the radius ...

radius $r = \sqrt{{\left(9 - 7\right)}^{2} + {\left(4 - 1\right)}^{2}} = \sqrt{13}$

Finally, use the general equation for a circle to fill in the values from the problem ...

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

${\left(x - 1\right)}^{2} + {\left(y - 7\right)}^{2} = 13$

hope that helped