Question

question 1 (multiple choice worth 1 points) (07.03r mc) using the following equation, find the center and radius: $x^2 + 2x + y^2 + 4y = 20$ 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 question 2 (multiple choice worth

Explanation:

Step1: Group x and y terms

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

Step2: Complete the square for x

$x^2 + 2x + 1 = (x+1)^2$, add 1 to right side:
$y^2 + 4y + (x+1)^2 = 20 + 1$

Step3: Complete the square for y

$y^2 + 4y + 4 = (y+2)^2$, add 4 to right side:
$(x+1)^2 + (y+2)^2 = 20 + 1 + 4$

Step4: Simplify right-hand side

$(x+1)^2 + (y+2)^2 = 25$

Step5: Match to circle standard form

Standard form: $(x-h)^2 + (y-k)^2 = r^2$, so $h=-1, k=-2, r=\sqrt{25}=5$

Answer:

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