+152 1)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?
2)The values of a function f(x) are given below:
Evaluate f^{-1}\left(f^{-1}(50)\times f^{-1}(10)+f^{-1}(26)\right)
+129852 1)
We have these equations
(-1 -h)^2 + (2 - k)^2 = r^2
(3 - h)^2 + k^2 = r^2
(9 - h)^2 + k^2 = r^2
Subtract the second equation from the 3rd and we have that
(9 - h)^2 - (3 - h)^2 = 0 simplify
h^2 - 18h + 81 - [ h^2 - 6h + 9 ] = 0
-12h + 72 =0
-12h = -72
h = 6
And equating the first two equations
(-1 - 6)^2 + (2 - k)^2 = (3 - 6)^2 + k^2
49 + k^2 - 4k + 4 = 9 + k^2
53 - 4k = 9
44 - 4k = 0
k = 11
So
(h, k) = (6, 11)
And h + k = 17
