Question

In the hyperbola $16x^2-9y^2=144$, find the equation to the diameter which is conjugate to the diameter whose equation is $x=2y$.

Answer 1

Two diameters of a hyperbola $y=mx$ and $y=m_{1}x$ are said to be conjugate if they follow the relation

$m{m}_1=\frac{b^2}{a^2}$

So here,

$m=\frac{1}{2}$

$\Rightarrow \frac{1}{2}{m}_1=\frac{16}{9}$

$\Rightarrow m_1=\frac{32}{9}$

Hence the equation of other diameter is

$y=\frac{32}{9}x$