Question

Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit.
x2 + 2x + y2 + 4y = 20

Answer 1

Answer:

( x+1)^2  + (y+2)^2 = 25

The center is (-1, -2) and the radius is 5

Step-by-step explanation:

x^2 + 2x + y^2 + 4y = 20

Complete the square

2/2 =1  1^2 =1  so add 1 for x     4/2 =2  2^2 = 4 so add 4 for y

x^2 +2x +1   +y^2 +4y+4 = 20 +1 +4

( x+1)^2  + (y+2)^2 = 25

(x+1) ^2 + (y+2)^2 = 5^2

(x - -1) ^2 + (y -  -2)^2 = 5^2

This is in (x-h)^2 + (y-k)^2 = r^2 form where (h,k) is the center and r is the radius

The center is (-1, -2) and the radius is 5