Parabolas: y=a*x^2 (a times x squared) for a>0 is being rotated around the y axis.

[nataliexyz]

The graph y=a*x^2 (a times x squared) for a>0 is being rotated around the y axis.
Someone wants to put a sphere inside the rotated parabola, touching its vertex.

I need to show all possible radii for the sphere dependent on the parameter a.

i understand the question, but I have no idea where I could possibly start and how to calculate r in this case.

Thank you ever so much for your help.

 

[Deleted member 4993]

The graph y=a*x^2 (a times x squared) for a>0 is being rotated around the y axis.
Someone wants to put a sphere inside the rotated parabola, touching its vertex.

I need to show all possible radii for the sphere dependent on the parameter a.

i understand the question, but I have no idea where I could possibly start and how to calculate r in this case.

Thank you ever so much for your help.

First draw an approximate sketch.

Then draw a tangent line to the parabola.

Locate the y-intercept of the line - that will be the center of the sphere.

continue...