There exists a circle C with radius 5, passing through the point (3,2), such that the center of C lies on the line x=7 and has positive y-coordinate. C is the graph of the equation x^2 + ax + y^2 + by + c = 0, where a,b,c, are integers (not necessarily positive). Find a+b+c.
i think the answer might be 25, not sure tho
+129845 Since it passes through (3,2) with the center at (7,y) we have
(3 - 7)^2 + ( 2 - y)^2 = 5^2
16 + (2 - m)^2 = 25
(2 - y)^2 = 25 -16
(2 - y)^2 = 9 take the NEGATIVE square root
2 - y = -3 rearrange as
5 = y
The center is ( 7, 5) and we have the equation of a circle
(x - 7)^2 + ( y - 5)^2 = 25
x^2 -14y + 49 + y^2 - 10y + 25 = 25
x^2 - 14y + y^2 -10y + 49 = 0
a = -14 b = -10 c = 49 and their sum = 25
And you are correct !!!!
