An inequality problem

Algebra Level 3

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.