Question

How do you find the center-radius form of the equation of the circle having a diameter with endpoints (0, -8) and (-6,0)?

Answer 1

Use `h = (x_0 + x_1)/2 and k = (y_0 + y_1)/2`to find the center. Substitute the center and one of the points into the general form, to find the radius.

Explanation:

Find the center:

`h = (0 + -6)/2 = -3`

`k = (-8 + 0)/2 = -4`

Substitute the center and a point into the equation for a circle:

`(0 - -3)^2 + (-8 - -4)^2 = r^2`

Solve for r:

`9 + 16 = r^2`

`r^2 = 25`

`r = 5`

The equation of the circle is:

`(x - -3)^2 + (y - -4)^2 = 5^2`