Answer:
[tex]x^2+y^2=81[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The radius of the circle is the distance between the center and any point on the circle
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have the points
(0,0) and (0,-9)
substitute in the formula
[tex]r=\sqrt{-9-0)^{2}+(0-0)^{2}}[/tex]
[tex]r=\sqrt{-9)^{2}+(0)^{2}}[/tex]
[tex]r=9/ units[/tex]
step 2
Find the equation of the circle
The equation of the circle in center radius form is equal to
[tex](x-h)^2+(y-k)^2=r^2[/tex]
we have
[tex](h,k)=(0,0)\\r=9\ units[/tex]
substitute
[tex](x-0)^2+(y-0)^2=9^2[/tex]
[tex]x^2+y^2=81[/tex]
