Question

Find the length of sub normal of parabola $y^2=12x$ at $(3,6)$.

• A. 6
• B. 8
• C. 10
• D. 12

Answer 1

Answer: (A)

6

$y^2=12x$

$\therefore \frac{dy}{dx}=\frac{6}{y}$

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

$=\left|y\right(\frac{6}{y}\left)\right|=6$

So, the length of subnormal at any point on the parabola is independent of the co-ordinates of the point and is equal to 6 units

So, the answer is option (A).