Answer:
The circle has radius = 9 units, and its equation is:
[tex]x^2+y^2=81[/tex]
The parabola has equation of the form:
[tex]y=a\,x^2+9[/tex]
with [tex]a[/tex] being a positive number
Step-by-step explanation:
Given the characteristics of the two figures (circle and parabola) as described,
since the parabola intersects the circle at a single point (it vertex) then the radius of the circle centered at the origin must be 9. that makes the equation of the circle to have the following standard form;
[tex]x^2+y^2=9^2\\x^2+y^2=81[/tex]
Since there is no other info regarding the parabola, the most one can say about the equation of the parabola, is that in vertex form, the parabola's equation must be of the form:
[tex]y=a\,(x-x_{vertex})^2+y_{vertex}\\y=a\,(x-0)^2+9\\y=a\,x^2+9[/tex]
with [tex]a[/tex] being a positive number.
