Question

Need help ASAP please and thank you

Answer 1

Answer:

$(x + 4)^2 + (y - 1)^2 = 81$

Step-by-step explanation:

The standard of the equation of a circle is:

$(x - h)^2 + (y - k)^2 = r^2$ 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.

$8x + x^2 - 2y = 64 - y^2$

Move all variables to the left side by addition or subtraction.

$x^2 + 8x + y^2 - 2y = 64$

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.

$x^2 + 8x + 16 + y^2 - 2y + 1 = 64 + 16 + 1$

$(x + 4)^2 + (y - 1)^2 = 81$