How do you graph x^2+y^2-8x+6y+16=0?

1 Answer
Nov 15, 2016

Set your compass to a radius of 3, put the centerpoint at (4, -3), and draw a circle.

Explanation:

This is a circle. To find the center and the radius, we must complete the squares for both x terms and y terms:

Add h^2 + k^2 -16 to both sides:

x^2 - 8x + h^2 + y^2 + 6y + k^2 = h^2 + k^2 - 16

Use the linear x term to find the value of h by setting it equal to -2xh:

-2hx = -8x

h = 4

Substitute (x - 4)^2 for the x terms on the left and 16 for h^2 on the right:

(x - 4)^2 + y^2 + 6y + k^2 = 16 + k^2 - 16

Use the linear y term to find the value of k by setting it equal to -2yk:

-2yk = 6y

k = -3

Substitute (y - -3)^2 for the y terms on the left and 9 for k^2 on the right:

(x - 4)^2 + (y - -3)^2 = 16 + 9 - 16 = 9 = 3^2

The final equation is:

(x - 4)^2 + (y - -3)^2 = 3^2

This is a circle with a center of (4, -3) and a radius of 3.