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 [tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex], 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 [tex]= 3-0=3[/tex] units.
So for the given circle, (h, k) is (0, -3) and r is 3 units.
So the equation becomes [tex](x-0)^{2}+(y-(-3))^{2}=3^{2}[/tex].
The standard equation for the circle is [tex]x^{2}+(y+3)^{2}=9.[/tex]
