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:

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

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

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

$l = \sqrt{100 + 576}$

$l = \sqrt{676} = 26$

Radius:

$radius = \frac{diameter}{2} = \frac{26}{2} = 13$

Midpoint:

$x(m) = \frac{x + x}{2} = \frac{6 - 4}{2} = \frac{2}{2} = 1$

$y(m) = \frac{y + y}{2} = \frac{16 - 8}{2} = \frac{8}{2} = 4$

I(1,4)

Equation of the circle:

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

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