If area of quadrilateral formed by tangents drawn at ends of latus rectum of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is equal to square of distance between centre and one focus of hyperbola, then $e^3$ is ($e$ is eccentricity of hyperbola)
If area of quadrilateral formed by tangents drawn at ends of latus rectum of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is equal to square of distance between centre and one focus of hyperbola, then $e^3$ is ($e$ is eccentricity of hyperbola)
- A
$2\sqrt 2$
- B
$2$
- C
$3$
- D
$8$
Similar Questions
The distance between the directrices of a rectangular hyperbola is $10$ units, then distance between its foci is
The distance between the directrices of a rectangular hyperbola is $10$ units, then distance between its foci is
The line $3x - 4y = 5$ is a tangent to the hyperbola ${x^2} - 4{y^2} = 5$. The point of contact is
The line $3x - 4y = 5$ is a tangent to the hyperbola ${x^2} - 4{y^2} = 5$. The point of contact is
If the tangents drawn to the hyperbola $4y^2 = x^2 + 1$ intersect the co-ordinate axes at the distinct points $A$ and $B$, then the locus of the mid point of $AB$ is
If the tangents drawn to the hyperbola $4y^2 = x^2 + 1$ intersect the co-ordinate axes at the distinct points $A$ and $B$, then the locus of the mid point of $AB$ is
- [JEE MAIN 2018]
The product of the perpendiculars drawn from any point on a hyperbola to its asymptotes is
The product of the perpendiculars drawn from any point on a hyperbola to its asymptotes is
The equation of the tangent at the point $(a\sec \theta ,\;b\tan \theta )$ of the conic $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, is
The equation of the tangent at the point $(a\sec \theta ,\;b\tan \theta )$ of the conic $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, is