Question

The equation of a circle is given below:

Answer 1

Given:

The equation of the circle is

We need to determine the center and radius of the circle.

Center:

The general form of the equation of the circle is

where (h,k) is the center of the circle and r is the radius.

Let us compare the general form of the equation of the circle with the given equation  to determine the center.

The given equation can be written as,

Comparing the two equations, we get;

(h,k) = (0,-4)

Therefore, the center of the circle is (0,-4)

Radius:

Let us compare the general form of the equation of the circle with the given equation  to determine the radius.

Hence, the given equation can be written as,

Comparing the two equation, we get;

Thus, the radius of the circle is 8