Question

Find the equation to the hyperbola, referred to its axes as axes of coordinates, whose transverse and conjugate axes are respectively $3$ and $4$.

Answer 1

For a hyperbola with equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, transverse axis is given by $2a$ and conjugate axis by $2b$.

Given :- $2a=3$

$\Rightarrow a=\frac{3}{2}$

$\&2b=4$

$\Rightarrow b=2$

$\therefore$ The hyperbola will have equation $\frac{4x^2}{9}-\frac{y^2}{4}=1$

$\Rightarrow 16x^2-9y^2=36$ is the equation of hyperbola