Question

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

Answer 1

`(x - 1)^2 + (y - -2.5)^2 = (sqrt(221)/2)^2`

Explanation:

The radius half of the distance between the two points:

`r = (1/2)sqrt((6 - -4)^2 + (-8 - 3)^2)`

`r = (1/2)sqrt((10)^2 + (-11))`

`r = 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:

`(-4 + 5, 3 - 5.5) = (1, -2.5)`

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

`(x - 1)^2 + (y - -2.5)^2 = (sqrt(221)/2)^2`