Complete the square to find the center and the radius of the circle?

Question

Complete the square to find the center and the radius of the circle: 3x^2 +3y^2 -6x +30y +15 =0

Answer 1

' the mathemagician' obviously meant radius = √ 21

Answer 2

First, take out the common factor of 3 from each term so the equation becomes:

x^2 + y^2 - 2x + 10y + 5 = 0

Then, reorder the terms so that you can complete the square-

x^2 - 2x       + y^2 + 10y      = -5

Completing the square for each variable

x^2 - 2x + 1 + y^2 + 10y + 25 = -5 + 26

(x - 1)^2 + (y + 5)^2 = (sqrt 26)^2

The center is at (1,-5) and the radius is sqrt 26