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. $x$

Answer 1

Answer: (B)

$y^2$

Length of subtangent $=\frac{y}{\left[dy/dx\right]}$

Length of subnormal $=y\frac{dy}{dx}$

$\therefore$ Product of length of subtangent & subnormal

$=\frac{y}{dy/dx}\times y\frac{dy}{dx}$

$=y^2$