Question

A circle on the Coordinate plane has a diameter with endpoints at (6,8) and (15,8). What are the coordinates of the center of the circle? What is the radius of the circle? Identify the coordinates of another point on the circle. Explain how you found your answer.

Answer 1

midpoint of diameter
= ( (6+15)/2 , (8+8)/2)
= ( 21/2 , 8)

equation:
(x-21/2)^2 + (y-8)^2 = r^2
plug in (6,8)
81/4 + 0 = r^2

(x-21/2)^2 + (y-8)^2 = 81/4

any other point?
how about the y-intercept, let x = 0
441/4 + (y-8)^2 = 81/4
y-8 = ±√90 = ±3√10
y = 8 ±√10

so (0, 8+3√10) and (0,8-3√10) are two more points