Let the foci of a hyperbola be $(1,14)$ and $(1,-12)$. If it passes through the point $(1,6)$, then the length of its latus-rectum is :

  • [JEE MAIN 2025]
  • A
    $\frac{25}{6}$
  • B
    $\frac{24}{5}$
  • C
    $\frac{288}{5}$
  • D
    $\frac{144}{5}$

Similar Questions

If the line $y\, = \,mx\, + \,7\sqrt 3 $ is normal to the hyperbola $\frac{{{x^2}}}{{24}} - \frac{{{y^2}}}{{18}} = 1,$ then a value of $m$ is 

  • [JEE MAIN 2019]

If $(a -2)x^2 + ay^2 = 4$ represents rectangular hyperbola, then $a$ equals :-

Find the equation of the hyperbola satisfying the give conditions: Vertices $(0,\,\pm 3),$ foci $(0,\,±5)$

If the straight line $x\cos \alpha + y\sin \alpha = p$ be a tangent to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, then

The equation of the transverse and conjugate axis of the hyperbola $16{x^2} - {y^2} + 64x + 4y + 44 = 0$ are