An inequality problem

Algebra Level 4

Let $a,b,x,y$ be real numbers such that $a^2 +b^2 =81$ , $x^2 + y^2 = 121$ and $ax+by=99$ .

Then what is the set of all possible values of $ay-bx$ ?

Its an old KVPY Problem. You can try other such problems here -

KVPY problems.