How to write a Perspective function in cvx? (Moderator note: this is non-convex because underlying function in this post is non-convex)

Hello. I am relatively new in cvx.
I have the function: f(x,y)=1/(x^2+y^2 ).
I compute the Hessian and I believe it is a convex function on (x,y).
If it is convex (cross-finger). Then, I would like to write its perspective function in the cvx format:
t/((x/t)^2+(y/t)^2 ).
So, my question is, assuming that f(x,y)=1/(x^2+y^2 ) is convex. How can I write its perspective function using the cvx rules?

1/(x^2 + y^2) is not convex. Its Hessian has one negative eigenvalue and one positive eigenvalue for all values of x and y.

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