If the length of the transverse and conjugate axes of a hyperbola are $8$ and $6$ respectively,then the difference of the focal distances of any point on the hyperbola will be

Let $P(3,3)$ be a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$. If the normal to it at $P$ intersects the $x$-axis at $(9,0)$ and $e$ is its eccentricity,then the ordered pair $(a^{2}, e^{2})$ is equal to

$A$ point on the curve $\frac{x^2}{A^2} - \frac{y^2}{B^2} = 1$ is

The length of the latus rectum of the hyperbola $9x^2 - 16y^2 - 18x - 32y - 151 = 0$ is

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 $a+b=$

The line $2x + y = 1$ is tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If this line passes through the point of intersection of the nearest directrix and the $x$-axis,then the eccentricity of the hyperbola is