Question

Determine the center and radius of the following circle equation:

x2 + y2 – 12x + 12y + 23 = 0
Help ASAP pls!!!
*It’s hw*

Answer 1

• The center = (a, b) = (6, -6)

• r = 7

Explanation:

Given the equation

`x^2\:+\:y^2\:-\:12x\:+\:12y\:+\:23\:=\:0`

We know that a circle equation with a radius 'r', centered at (a, b)

`\left(x-a\right)^2+\left(y-b\right)^2=r^2`

Rewriting
`x^2\:+\:y^2\:-\:12x\:+\:12y\:+\:23\:=\:0` in the form of the standard circle equation

`\left(x-6\right)^2+\left(y-\left(-6\right)\right)^2=7^2`

Thus,

• The center = (a, b) = (6, -6)

• r = 7