jmc

Question

This circle passes through the points (-1, 2), (3,0) and (9,0). The center of the circle is at (h,k). What is the value of h+k?

Accepted Answer

The center of the circle must lie on the perpendicular bisector of the points

(3, 0)

and

(9, 0),

which is the line

x = 6,

so

h = 6.

Thus, the center of the circle is

(6, k) .

This point must be equidistant to

(- 1, 2)

and

(3, 0),

so

7^{2} + (k - 2)^{2} = 9 + k^{2} .

This gives us

k = 11.

Hence,

h + k = 6 + 11 = 17 .