# How do you write an equation with endpoints of a diameter are (-4,3) and (6,-8)?

Oct 13, 2016

${\left(x - 1\right)}^{2} + {\left(y - - 2.5\right)}^{2} = {\left(\frac{\sqrt{221}}{2}\right)}^{2}$

#### Explanation:

The radius half of the distance between the two points:

$r = \left(\frac{1}{2}\right) \sqrt{{\left(6 - - 4\right)}^{2} + {\left(- 8 - 3\right)}^{2}}$

$r = \left(\frac{1}{2}\right) \sqrt{{\left(10\right)}^{2} + \left(- 11\right)}$

$r = \frac{\sqrt{221}}{2}$

Please notice that to go from the first point to the second, we move right 10 and down 11. The center will be halfway between them, right 5 and down 5.5 from the first point:

$\left(- 4 + 5 , 3 - 5.5\right) = \left(1 , - 2.5\right)$

We may, now, write the equation of the circle:

${\left(x - 1\right)}^{2} + {\left(y - - 2.5\right)}^{2} = {\left(\frac{\sqrt{221}}{2}\right)}^{2}$