Question

Find the equation to the hyperbola, referred to its axes as axes of coordinates, whose conjugate axis is $5$ and the distance between whose foci is $13$,

Answer 1

For a hyperbola with conjugate axis $2b=5$, the distance between two foci is given as $2c$, where $c^2=a^2+b^2$

$\Rightarrow a^2=c^2-b^2$

$\Rightarrow a^2=(6\cdot 5{)}^2-(2\cdot 5{)}^2$

$\Rightarrow a^2=36$

Equation of the hyperbola will be given by $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

on simplifying we get the equation of hyperbola as $25x^2-144y^2=900$