Question

Find the length of sub normal of parabola $y^2=4x$ at $(1,1)$.

• A. 2
• B. 4
• C. 8
• D. 10

Answer 1

Answer: (A)

2

$y^2=4x$

$\therefore \frac{dy}{dx}=\frac{2}{y}$

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

$=\left|y\right(\frac{2}{y}\left)\right|=2$

So, the length of subnormal at any point is independent of the co-ordinates of the point and is equal to 2 units.

So, the answer is option (A).