Answer: the correct option is
(D) (-7, -1), 6 units.
Step-by-step explanation: We are given to find the co-ordinates of the center and the length of the radius of the following circle :
[tex]x^2+y^2+14x+2y+14=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the STANDARD equation of a circle with center at the point (h, k) and radius of length r units is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2+14x+2y+14=0\\\\\Rightarrow (x^2+14x+49)+(y^2+2y+1)+14-49-1=0\\\\\Rightarrow (x+7)^2+(y+1)^2-36=0\\\\\Rightarrow (x+7)^2+(y+1)^2=36\\\\\Rightarrow (x-(-7))^2+(y-(-1))^2=6^2.[/tex]
Comparing the above equation with the standard equation of a circle, we get
center, (h, k) = (-7, -1) and radius, r = 6 units.
Thus, (D) is the correct option.
