Question

Which of the following is the equation of the circle whose endpoints of diameter lie on (-2,4) and (4,-8)?

Answer 1

`(x-1)^2+(y+2)^2=45`

Explanation:

There aren't any choices offered but it doesn't matter.

The center is the midpoint of the diameter:

`C(a,b) = ((-2 + 4)/2 , (4+ -8)/2) = (1,-2)`

The squared radius is the squared distance from the center to one of the points:

`r^2 = (-2 - 1)^2 + (4 - -2)^2 = 3^2+6^2=45`

The equation in general is `(x-a)^2 + (y-b)^2 = r^2` or in our case

`(x-1)^2+(y+2)^2=45`

We check the second point:

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