Question

Find the equation of the line normal to the hyperbola $x^2-3y^2=144$ at the positive end of the latusrectum.

Answer 1

Given that

$x^2-3y^2=144$

$\Rightarrow \frac{x^2}{144}-\frac{3y^2}{144}=\frac{144}{144}$ [Divide both sides by $\frac{1}{144}$]

$\Rightarrow \frac{x^2}{144}-\frac{y^2}{38}=1$ [divide $144$ by $3$ and $144$ by $144$]

Which is the required equation of the hyperbola.