For what value of c will the circle with equation x^2 + 8x + y^2 + 6y + c = 0 have a radius of length \(3\)?
+1224 x^2 + 8x + y^2 + 6y = -c
(x + 4)^2 + (y + 3)^2 = -c + 16 + 9 = -c + 25
The equation of a circle is (x - h)^2 + (y - k)^2 = r^2. So, we want:
-c + 25 = 3^2 = 9
c = 16.
+36916 x^2 + 8x + y^2 + 6 y = - c complete the square for x and y
(x+4)^2 + (y+3)^2 = 16 + 9 - c red part = radius ^2
25 - c = 3^2
- c = -16
c = 16
