The equation of the circle has the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where
(h,k) are the coordinates of the center of the circle
r is the radius of the circle
If the center of the circle is at the origin, (0,0) and it passes through the point (0,-9), since both x-coordinates are equal, the length of the radius is equal to the difference between the y-coordinates of the center and the given point:
[tex]r=y_{\text{center}}-y_{point=}0-(-9)=0+9=9[/tex]
The radius is 9 units long.
Replace the coordinates of the center and the length of the radius in the formula:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=9^2 \\ x^2+y^2=81 \end{gathered}[/tex]
So, the equation of the circle that has a center in the origin and passes through the point (0.-9) is:
[tex]x^2+y^2=81[/tex]
