(4,1) lies on the circle, so Call that eq: 1.

(6,5) lies on the circle, so Call that eq: 2

(h,k) is the center of the circle, and therefore must lie on the line that passes through the center. 4h + k = 16 and thus k = 16-4h eq: 3

Set 1 = 2 since both = r squared.

Expand the squared binomials: .

Subtract h squared and k squared from both sides, and combine like terms.

17 - 8h - 2k = 61 -12h - 10k

4h = 44 - 8k so h = 11-2k Substitute that into eq:3 and solve it for k

k = 16 - 4(11-2k) = 16 - 44 +8k = 28+8k

-7k =28

k = -4

h = 11-2k = 11-2(-4) = 11+8 = 19.

The center of the circle is (19,-4) and thus the equation is:

Use one of the given points to find r. Use (4,1).

The equation is

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