The equation of the pair of asymptotes of the hyperbola $\frac{(x-3)^2}{3}-\frac{(y-2)^2}{2}=1$ is

If $L_1=0$ and $L_2=0$ are the asymptotes of the hyperbola $9x^2-4y^2+36x+8y-4=0$,then the product of the perpendicular distances from the point $(1,1)$ to the lines $L_1=0$ and $L_2=0$ is

Let $P$ be a point on the hyperbola $H: \frac{x^2}{9}-\frac{y^2}{4}=1$,in the first quadrant such that the area of the triangle formed by $P$ and the two foci of $H$ is $2 \sqrt{13}$. Then,the square of the distance of $P$ from the origin is

If the normal to the rectangular hyperbola $x^2-y^2=1$ at the point $P$ with parameter $\theta_1 = \frac{\pi}{4}$ meets the curve again at $Q$ with parameter $\theta_2$,then find the value of $\sec^2 \theta_2 + \tan \theta_2$.

If one of the roots of the equation $x^2 - 5x - 14 = 0$ is the length of the semi-conjugate axis of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ and the square of the other root is the semi-transverse axis,then the focus of the hyperbola that lies on the positive $x$-axis is

Let the ellipse $E: \frac{x^{2}}{144}+\frac{y^{2}}{169}=1$ and the hyperbola $H: \frac{x^{2}}{16}-\frac{y^{2}}{\lambda^{2}}=-1$ have the same foci. If $e$ and $L$ respectively denote the eccentricity and the length of the latus rectum of $H$, then the value of $24(e+L)$ is: