Question

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

• A. $8$
• B. $4$
• C. $9$
• D. None of these

Answer 1

Answer: (B)

$4$

$y^2=8x$

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

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

$=\left|\frac{y^2}{4}\right|$

So, the length of subtangent at $(2,4)=\left|\frac{4^2}{4}\right|=4$ units

So, the answer is option (B).