Question

The equation of a circle is given below.

Answer 1

Given:

The equation of the circle is $x^2+(y+4)^2=64$

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

Center:

The general form of the equation of the circle is $(x-h)^2+(y-k)^2=r^2$

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 $x^2+(y+4)^2=64$ to determine the center.

The given equation can be written as,

$(x-0)^2+(y+4)^2=64$

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 $x^2+(y+4)^2=64$ to determine the radius.

Hence, the given equation can be written as,

$x^2+(y+4)^2=8^2$

Comparing the two equation, we get;

$r^2=8^2$

 $r=8$

Thus, the radius of the circle is 8