Completing the Square to Find Center & Radius

Question

Rewrite the equation in graphing form by completing the square. Then state the center and the radius of the circle.

`y^{2}+2x+x^{2}=24y-120`

Answer 1

If we take half of b and square it (twice in this case), and add to both sides, we complete the square.

x² + 2x + 1 + y² - 24y + 144 = -120 + 1 + 144

(x + 1)² + (y - 12)² = 25

So, our center is (-1,12) and our radius is 5.

Yes, -5 is a square root of 25 but we don't measure using negatives unless we're considering net distance. If I walk 5 feet forward and 5 feet backward, I travelled 10 total feet although my net distance is zero, right?

Hope this helps!