The equation of the circle that passes through (-1,6) and which has a center at (2,3) can be written as x^2 + y^2 + Ax + By + C = 0. Find A times B times C.
+23246 Equation of a circle: (x - h)2 + (y - k)2 = r2 where the center is (h, k) and the radius is r.
Since the center is (2,3) h = 2 and k = 3.
To find the radius we need to know the distance from (-1,6) to (2,3).
Using the distance formula: r = sqrt( (2 - -1)2 + (3 - 6)2 ) = sqrt( (3)2 + (-3)2 ) = sqrt( 9 + 9 ) = sqrt( 18 )
Since r = sqrt( 18 ) ---> r2 = 18
So, our equation is: (x - 2)2 + (y - 3)2 = 18
Multiplying this out: (x2 - 4x + 4) + (y2 - 6y + 9) = 18
The equation for the circle is: x2 + y2 - 4x - 6y - 5 = 0
From here, pick out A, B, and C, and multiply them together.
