Hyperbola

The locus of the point of intersection of the tangents at the end points of normal chords of the hyperbola $$\cfrac { { x }^{ 2 } }{ { a }^{ 2 } } -\cfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1$$:
Find the equation of the tangent to the hyperbola $$4x^2\, -\, 9y^2\,=\, 1$$, which is parallel to the line $$4y = 5x + 7$$
If a rectangular hyperbola $$(x - 1) (y - 2) = 4$$ cuts a circle $$x^2 + y^2 - 7x - 9y + c = 0$$ at points $$(3, 4), (5, 3), (2, 6)$$ and point $$P(u, v)$$, then the value of $$9(u + v)$$ is equal to

The asymptotes of the hyperbola $$36{y}^{2}-25{x}^{2}+900=0$$, are: