You must complete the square:
x^2 + 6x + y^2 - 8y = 56
For any (x-c), (x+c)^2 = x^2 + 2cx + c^2
Now compare x^2 + 6x to x^2 + 2cx + c^2. You are missing c^2. You can find c, though, by 6x:
6x = 2cx
6 = 2c
3 = c
So c^2 = 9.
The perfect square is (x+c)^2 = (x+3)^2 because you found that c=3
You do not have a 9 in the equation - but you can add 0:
x^2 + 6x + 9 - 9 + y^2 - 8y = 56
(x+3)^2 -9 + y^2 - 8y = 56
Move the 9 over to the other side
(x+3)^2 + y^2 - 8y = 64
Try doing the same with y.
find the center (h,k) and radius r of the circle with the given equation:
x^2 + y^2 + 6x - 8y = 56
1 answer
1 answer