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

The correct answer is D.

Step-by-step explanation:

Given:

General equation of second degree

x² + y² + 14 x + 2 y + 14 = 0

We must transform given equation to the canonical form from which we will read requested data.

The canonical form of the circle equation is:

(x - p) ² + (y - q) ² = r²

Where p and q are the coordinates of the center of the circle and r are radius. (p, q) = (x, y)

x² + 2 · x ·7 + 7² - 7² + y² + 2 · y · 1 + 1 - 1 + 14 = (x+7) ² + (y+1) - 49 - 1 + 14 = 0

(x + 7) ² + (y + 1) ² = 36

We see that p = - 7, q = - 1 and r = 6

God with you!