Question

A hyperbola with center at the origin, conjugate axis on y-axis, latus rectum 18/5 , distance between directrices (25√34)/17. Find its equation.

Answer 1

Equation format of a hyperbola whose conjugate axis is y-axis is

\[\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\]

Answer 2

Length of a Latus rectum of a hyperbola is \[\frac{2b^2}{a}\]

Answer 3

Equation of directrix is \[x=\pm \frac{25}{\sqrt{34}}=\pm \frac{b}{e} \]

Answer 4

And relation between a, b & c is \[b^2=a^2(e^2-1)\] where 'e' is eccentricity.

Answer 5

I dont know how to equate.