# The product of the lengths of subtangent and subnormal at any point x, y on the curve is

A. ${x^2}$

B. ${y^2}$

C. A constant

D. x

Last updated date: 24th Mar 2023

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Answer

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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.

Complete step-by-step answer:

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.

Complete step-by-step answer:

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.

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