Question

A circle has (6, -8) and (-4, 16) as endpoints of a diameter.

Find the center and radius of the circle.
Graph the circle.
Write the standard equation of the circle.

Answer 1

Length of the diameter:

`l = \sqrt{(x - x) {}^(2) + (y - y) {}^(2) }`

`l = \sqrt{( - 4 - 6) {}^(2) + (16 + 8) {}^(2) }`

`l = \sqrt{( - 10) {}^(2) + (24) {}^(2) }`

`l = √(100 + 576)`

`l = √(676) = 26`

Radius:

`radius = (diameter)/(2) = (26)/(2) = 13`

Midpoint:

`x(m) = (x + x)/(2) = (6 - 4)/(2) = (2)/(2) = 1`

`y(m) = (y + y)/(2) = (16 - 8)/(2) = (8)/(2) = 4`

I(1,4)

Equation of the circle:

`(x - 1) {}^(2) + (y - 4) {}^(2) = 14 {}^(2)`

`(x - 1) {}^(2) + (y - 4) {}^(2) = 196`