A little help with calculus cross section project?

So for a cross section calculus project I need to find equations that when combined make a tennis racket looking base. So far the equations I've used are:

y= +/- √(9((-x^2)+1))

and

y= +/- 1.81e^x

So my questions are:

*How do I make the equation so that the handle of the tennis racket does not look thin as a stick? So, how do I make the handle on both sides are not so close to the x-axis?

*Also, if it is possible, how do you stop the y= +/- 1.81e^2 right when it intersects with the "oval", so it doesn't go onto infinity?

Thanks for your help!