If the two tangents drawn on hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ in such a way that the product of their gradients is ${c^2}$, then they intersects on the curve
If the two tangents drawn on hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ in such a way that the product of their gradients is ${c^2}$, then they intersects on the curve
- A
${y^2} + {b^2} = {c^2}({x^2} - {a^2})$
- B
${y^2} + {b^2} = {c^2}({x^2} + {a^2})$
- C
$a{x^2} + b{y^2} = {c^2}$
- D
None of these
Similar Questions
Let $a>0, b>0$. Let $e$ and $\ell$ respectively be the eccentricity and length of the latus rectum of the hyperbola $\frac{ x ^{2}}{ a ^{2}}-\frac{ y ^{2}}{ b ^{2}}=1$. Let $e ^{\prime}$ and $\ell^{\prime}$ respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If $e ^{2}=\frac{11}{14} \ell$ and $\left( e ^{\prime}\right)^{2}=\frac{11}{8} \ell^{\prime}$, then the value of $77 a+44 b$ is equal to
Let $a>0, b>0$. Let $e$ and $\ell$ respectively be the eccentricity and length of the latus rectum of the hyperbola $\frac{ x ^{2}}{ a ^{2}}-\frac{ y ^{2}}{ b ^{2}}=1$. Let $e ^{\prime}$ and $\ell^{\prime}$ respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If $e ^{2}=\frac{11}{14} \ell$ and $\left( e ^{\prime}\right)^{2}=\frac{11}{8} \ell^{\prime}$, then the value of $77 a+44 b$ is equal to
- [JEE MAIN 2022]
The length of the latus rectum of the hyperbola $25x^2 -16y^2 = 400$ is -
The length of the latus rectum of the hyperbola $25x^2 -16y^2 = 400$ is -
Tangents are drawn to the hyperbola $4{x^2} - {y^2} = 36$ at the points $P$ and $Q.$ If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\Delta PTQ$ is :
Tangents are drawn to the hyperbola $4{x^2} - {y^2} = 36$ at the points $P$ and $Q.$ If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\Delta PTQ$ is :
- [JEE MAIN 2018]
If $\frac{{{{\left( {3x - 4y - z} \right)}^2}}}{{100}} - {\frac{{\left( {4x + 3y - 1} \right)}}{{225}}^2} = 1$ then
length of latusrectum of hyperbola is
If $\frac{{{{\left( {3x - 4y - z} \right)}^2}}}{{100}} - {\frac{{\left( {4x + 3y - 1} \right)}}{{225}}^2} = 1$ then
length of latusrectum of hyperbola is
If angle between asymptotes of hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{3} = 4$ is $\frac {\pi }{3}$ , then its conjugate hyperbola is
If angle between asymptotes of hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{3} = 4$ is $\frac {\pi }{3}$ , then its conjugate hyperbola is