Question

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

Answer:

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!!!