Question

Where is the center of the circle and what is its radius

Answer 1

(3, -4) and r = 3

Explanation:

The center of a circle can be found using the equation
`(x-h)^2 + (y-k)^2 = r^2` and is (h,k) from it. Notice h and k are the opposite value as in the equation.

First write the equation in this form.

`x^2 - 6x + ( ?)+ y^2 +8y + (?) + 16 = 0`

Complete the square with each variable to find what numbers should go in place of the question marks.

`(-6/2)^2 = -3^2 = 9`

`(8/2)^2 = 4^2 = 16`

Since 16 has already been added to the equation, just add 9 to both sides of the equation.

`x^2 - 6x + 9 + y^2 +8y + 16 = 9\\(x-3)^2 + (y+4)^2 = 9`

So the center is (3,-4) and the radius is 3.