29. (09.04 MC) Using the following equation, find the center and radius:
x2 + 2x + y2 + 4y = 20 (5 points)
The center is located at (1, 2), and the radius is 25.
The center is located at (-1, 2), and the radius is 25.
The center is located at (-1, -2), and the radius is 5.
The center is located at (1, 2), and the radius is 5.

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

Step-by-step explanation:

The general equation of a circle is given as

(x - a)^2 + (y - b)^2 = r^2

where

a and b are the centre of the circle and r is the radius

Given the equation

x2 + 2x + y2 + 4y = 20

add 1 ad 4 to both sides

x2 + 2x + 1 + y2 + 4y + 4 = 20 + 4 + 1

factorise

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

comparing with the general equation

a = -1, b = -2, r = 5 (all measured in units)