Center and Radius From a Circle Equation

Center and Radius from a Circle Equation

1. Rewrite the equation in standard circle form
   A circle equation is usually written as
   [ (x-h)^2+(y-k)^2=r^2 ]
   where the center is ((h,k)) and the radius is (r).

2. Identify the center
   Compare the given equation to the standard form. The numbers inside the squared terms tell you the center, with the signs reversed:

   • (x-h) means the x-coordinate is (h)
   • (y-k) means the y-coordinate is (k)

3. Find the radius
   The number on the right side is (r^2). Take the square root to get (r). Since radius is a distance, use the positive square root only.

4. Simplify carefully
   If the right side is a perfect square, the radius is an integer. If not, simplify the radical if possible.

Quick check

• Plug the center into the equation: it should make the left side equal 0.
• Square your radius and compare it to the right side.

Example pattern

If the equation looks like ((x-3)^2+(y+2)^2=25), then the center is ((3,-2)) and the radius is (5).