Given the equation $\frac{x^2} {3}-\frac {y^2} {12}=1 $ and a square with vertices on the hyperbola and sides parallel to the axis prove that every vertex has this property:
Let $A$ be the vertex, and $r$ the tangent to the hyperbola in the point $A$. If $M, N$ are the intersection of $r$ with the asymptotes $y=2x$ and $y=-2x$ than $MA\cong NA$.
I don't know how to prove this fact, is it general?
How many square of this type are there?