Answer:
[tex] (x + 4)^2 + (y - 1)^2 = 81 [/tex]
Step-by-step explanation:
The standard of the equation of a circle is:
[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex] where point (h, k) is the center of the circle, and r is the radius of the circle.
You need to complete the square for x and y.
[tex] 8x + x^2 - 2y = 64 - y^2 [/tex]
Move all variables to the left side by addition or subtraction.
[tex] x^2 + 8x + y^2 - 2y = 64 [/tex]
To complete a square, you need the square of half of the x or y term coefficient.
For x: 1/2 * 8 = 4; 4^2 = 16
For y: (1/2) * (-2) = -1; (-1)^2 = 1
We add 16 to complete the square in x and 1 to complete the square in x. We must add those numbers to both sides of the equation.
[tex] x^2 + 8x + 16 + y^2 - 2y + 1 = 64 + 16 + 1 [/tex]
[tex] (x + 4)^2 + (y - 1)^2 = 81 [/tex]
