Question

PLEASE HELPPPP 30 POINTS

Select the correct answer.
A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?

A.
(-7, -1), 36 units

B.
(7, 1), 36 units

C.
(7, 1), 6 units

D.
(-7, -1), 6 units

Answer 1

x^2 + y^2 + 14x + 2y + 14 = 0

Subtract 14 from both sides:

2 + y2 + 14x + 2y = -14

Complete the square for x^2 +14x:

(x+7)^2 -49

Now you have:

(x+7)^2 -49 +y^2+2y = -14

Complete the square for y^2 +2y:

(y+1)^2 -1

Now you have:

(x+7)^2 -49 + (y+1)^2 -1 = -14

Add 50 to each sides:

(x+7)^2 + (y+1)^2 = 36

The form of a circle is (x-h)^2 + (y-k)^2 = r^2

H and k are the center point and r is the radius.

H = -7, K = -1, r = √36 = 6

The answer is D. (-7, -1), 6 units