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

1 Answer
Jan 9, 2017

Answer:

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#