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# 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  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.
View Notes
Construction of Tangent to a Circle  Shapes of Total Product, Average Product and Marginal Product  Tangent of a Circle  The Language of Mathematics  A Guide to The Creation of The Perfect Writing  Length of Tangent  The Journey To the End of The Earth Summary  Introduction to the Composition of Functions and Inverse of a Function  Tangent to a Circle  Total Product, Average Product and Marginal Product  