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

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

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