Question

Using the following equation, find the center and radius of the circle: x^2 + y^2 +2x − 4y − 20 = 0

Answer 1

You have to complete the squares on both the x terms and the y terms in order to solve this. Move the 20 over to the other side so it's negative. Group the x terms together and complete the square to get (x^2+2x+1) and then do the same with the y terms: (y^2-4y+4). You have to add 1 and 4 to other side with the 20 to get a 25. Then create 2 perfect square binomials within each x and y value to get the vertex coordinates: (x+1)^2 + (y-2)^2 = 25. This tells us that the vertex is located at (-1, 2) and the radius is the square root of 25 which is 5.So the answer is the first choice above.