Question

If the length of the subnormal at any point of the curve is constant, then the eccentricity of this curve is _______

• A. $e=\sqrt{2}$
• B. $e>1$
• C. $0<e<1$
• D. $e=1$

Answer 1

The correct option is D $e=1$

$\left|y_{1}m\right|=a$

writing slope as $\frac{dy}{dx}$
$y\frac{dy}{dx}=\pm a$

$\Rightarrow \int ydy=\int \pm adx$

$\Rightarrow \frac{y^2}{2}=\pm a+c$
It is a parabola so $e=1$