Question

Please help!!!! I am about to fail !!

Answer 1

Given:

A circle with its center at (0, -3).

To find:

The standard equation for the given circle.

Solution:

The standard form of a circle is $(x-h)^{2}+(y-k)^{2}=r^{2}$, where (h, k) is the center of the circle and r is the radius of the circle.

The center of the given circle is at (0, -3).

We need to determine the radius of the circle. The center is at (0, -3) and a point with the same y coordinate is (3, -3).

The radius of the circle $= 3-0=3$ units.

So for the given circle, (h, k) is (0, -3) and r is 3 units.

So the equation becomes $(x-0)^{2}+(y-(-3))^{2}=3^{2}$.

The standard equation for the circle is $x^{2}+(y+3)^{2}=9.$