Courses
Courses for Kids
Free study material
Free LIVE classes
More LIVE
Join Vedantu’s FREE Mastercalss

# The product of the lengths of subtangent and subnormal at any point x, y on the curve isA. ${x^2}$ B. ${y^2}$ C. A constantD. x Verified
361.8k+ views
Hint:To solve this problem make use of the formula of length of subtangent and subnormal and find out the values and then multiply these two values and find their product. The length of the sub tangent is given by the formula.

Length of the sub tangent=$\dfrac{y}{{[dy/dx]}}$ and
The length of the subnormal is given by the formula =$y\dfrac{{dy}}{{dx}}$
We have been asked to find out the product of the length of subtangent and normal
=$\dfrac{y}{{dy/dx}} \times y\dfrac{{dy}}{{dx}}$
$= \dfrac{{ydx}}{{dy}} \times y\dfrac{{dy}}{{dx}}$
So, from this we get we get the product of the length of subtangent and subnormal
=${y^2}$

So, option B is the correct answer to this question

Note: When solving these type of problems, just make use of the standard formula of the required quantities and then modify it accordingly and find the required answer.
Last updated date: 24th Sep 2023
Total views: 361.8k
Views today: 7.61k