### Hyperbola

goals
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: