Question

The curve for which the normal at any point $(x,y)$ and the line joining origin to the points from the isosceles triangle with x-axis as base, is

• A. An ellipse
• B. A rectangular hyperbola
• C. A circle
• D. None of the above

Answer 1

Answer: (B)

A rectangular hyperbola

It is given that the $△OPG$ is an isosceles triangle.
Therefore, $OM=MG=$ subnormal
$\Rightarrow x=y\frac{dy}{dx}$
$\Rightarrow xdx=ydy$
On integration, we get $x^2-y^2=c$ which is rectangular hyperbola.