Question

Find the length of sub normal of parabola $y^2=8x$ at $(2,4)$.

• A. $4$
• B. $6$
• C. $8$
• D. None of the above

Answer 1

The correct option is A $4$

$y^2=8x$

$\therefore \frac{dy}{dx}=\frac{4}{y}$

Length of subnormal $=\left|y\right(\frac{dy}{dx}\left)\right|$

$=\left|y\right(\frac{4}{y}\left)\right|=4$

So, the length of subnormal at any point is independent of the co-ordinates of the point and is equal to 4 units.

So, the answer is option (A).