Question

# 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 =$y\dfrac{{dy}}{{dx}}$
=$\dfrac{y}{{dy/dx}} \times y\dfrac{{dy}}{{dx}}$
$= \dfrac{{ydx}}{{dy}} \times y\dfrac{{dy}}{{dx}}$
=${y^2}$