Question

The product of the lengths of subtangent and subnormal at any point $(x,y)$ of a curve is:

• A. $x^2$
• B. $y^2$
• C. a constant
• D. $x$
• E. $y$

Answer 1

Answer: (B)

$\because$ Length of sub tangent $=\frac{y}{\left(\frac{dy}{dx}\right)}$ and length of subnormal $=y\frac{dy}{dx}$ $\therefore$ Product of subtangent and subnormal $=\frac{y}{\left(\frac{dy}{dx}\right)}.y\frac{dy}{dx}=y^2$