Question

The general form of a circle is given as x^2 + y^2 + 4x - 12y + 4 = 0.

What are coordinates of the center of the circle?
What is the length of the radius of the circle?

Answer 1

If you can rewrite the formula as (x-a)² + (y-b)² = r², the center is at (a,b) and the radius is r.

If you work out this equation, and map it to the original, you will find that the +4x term hints that a = 2 (double product) and -12y hints that b=-6, and r=6.

So, the formula can be written as (x+2)² + (y-6)² = 6² and the center is at (-2,6) and the radius is 6.