Question

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?

Answer 1

(-7, -1), 6 units Is The Answer

Answer 2

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.