What is the equation of the circle?

Question

a circle has an endpoint of a diameter at (-2,4).if the diameter is perpendicular to a chord (which is not a diameter) whose endpoints are (6,8) and (6,0) find the equation of the circle.

Answer 1

equation: (x-3)^2 + (y-4)^2 = 25

circle's center is midpoint of a diameter with one end point (-2,4)

(x-h)^2 + (y-k)^2 = r^2 is the general formula

plug in (x,y) = (6,8) and (6,0)

(6-h)^2 +(8-k)^2 = r^2

(6-h)^2 + (0-k)^2 = r^2

subtract

-16k +64 = 0

k = 4, the circle has a y coordinate of 4 (h,4) same as the endpoint of the diameter

which almost makes no sense, no diameter ends at the center

but draw a diagram. the diameter endpoint is shifted horizontally from the center, either less than or greater than -2 but not equal to -2. the shift amount = r = d/2 = the radius = 5

h= -2 +5 = 3, center = (3,4)