The eccentricity of the hyperbola $-\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is:

If the equation of the tangent drawn at $(h, k)$ to the hyperbola $\frac{(x-1)^2}{1}-\frac{(y-2)^2}{2}=1$ is $x=2$,then $h+k=$

If the circle $x^{2}+y^{2}=a^{2}$ intersects the hyperbola $xy=c^{2}$ in four points $P(x_{1}, y_{1}), Q(x_{2}, y_{2}), R(x_{3}, y_{3})$ and $S(x_{4}, y_{4})$,then

If the straight line $(a-1)x - by + 4 = 0$ is normal to the hyperbola $xy = 1$, then which of the following does not hold?

Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$,parallel to the straight line $2x-y=1$. The points of contact of the tangents on the hyperbola are:
$(A) \left(\frac{9}{2\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
$(B) \left(-\frac{9}{2\sqrt{2}}, -\frac{1}{\sqrt{2}}\right)$
$(C) (3\sqrt{3}, -2\sqrt{2})$
$(D) (-3\sqrt{3}, 2\sqrt{2})$

Find the length of the latus rectum of the hyperbola $16x^2 - 9y^2 = 144$. (in $/3$)