For the hyperbola $\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 1$,which of the following remains constant with a change in $\alpha$?

$P(\theta)$ is a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{9} = 1$,$S$ is its focus lying on the positive $X$-axis and $Q = (0, 1)$. If $S Q = \sqrt{26}$ and $S P = 6$,then $\theta =$

Let the $X$-axis be the transverse axis and the $Y$-axis be the conjugate axis of a hyperbola $H$. Let $x^2+y^2=16$ be the director circle of $H$. If the perpendicular distance from the centre of $H$ to its latus rectum is $\sqrt{34}$,then $a+b=$

What is the area of the triangle formed by the lines $x - y = 0$,$x + y = 0$,and any tangent to the hyperbola $x^{2} - y^{2} = a^{2}$?

The equation of the normal at the point $(6, 4)$ on the hyperbola $\frac{x^2}{9} - \frac{y^2}{16} = 3$ is:

The locus of the point of intersection of the straight lines $\frac{x}{a} - \frac{y}{b} = m$ and $\frac{x}{a} + \frac{y}{b} = \frac{1}{m}$ is