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