Answer:
option d is correct.
center = (-7, -1)
r = 6
Step-by-step explanation:
The general equation of the circle is given by;
\((x-h)^2+(y-k)^2 = r^2\)
where;
(h, k) is the center of the circle
r is the radius of the circle respectively.
As per the statement:
A circle is described by the equation \(x^2 + y^2 + 14x + 2y + 14 = 0\)
then;
\((x^2+14x)+(y^2 + 2y) + 14 = 0\)
Using the completing the square:
\((x^2+14x+7^2-7^2)+(y^2 + 2y+1^2-1^2) + 14 = 0\)
⇒\((x+7)^2 - 49 + (y+1)^2 - 1 + 14 = 0\)
⇒ \((x+7)^2+(y+1)^2 -36 = 0\)
Add 36 to both sides we have;
\((x+7)^2+(y+1)^2=36\)
On comparing with the general equation of circle:
we get;
h = -7 , k = -1 and \(r^2 = 36\)
⇒\(r = 6\)
Therefore, the coordinate of the center of the circle is (-7, -1) and length of the radius of the circle is 6
