At what angle do the curves $x^2 - y^2 = 5$ and $\frac{x^2}{18} + \frac{y^2}{8} = 1$ intersect at any common point?

Tangents are drawn from the point $P(3, 4)$ to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,touching the ellipse at points $A$ and $B$. The orthocenter of $\Delta PAB$ is:

Consider two families of curves $y^2=4ax$ ($a$ is a parameter) and $x^2+\frac{y^2}{2}=c^2$ ($c$ is a parameter). If one curve from each family is chosen, then the angle between those two curves is

Tangents are drawn from the point $P\ (3, 4)$ to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,touching the ellipse at points $A$ and $B$. Find the coordinates of $A$ and $B$.

At the point of intersection of the rectangular hyperbola $xy = c^2$ and the parabola $y^2 = 4ax$,tangents to the rectangular hyperbola and the parabola make an angle $\theta$ and $\phi$ respectively with the $X$-axis. Then:

The graph of the conic $x^2-(y-1)^2=1$ has one tangent line with positive slope that passes through the origin. If the point of tangency is $(a, b)$,then find the value of $\sin^{-1}\left(\frac{a}{b}\right)$.