Question

The length of subtangent at any point of the curve $\log y=25x$ is

• A. constant
• B. proportional to $y$
• C. zero
• D. proportional to $x$

Answer 1

The correct option is A constant

${\log }_{e}y=25x\Rightarrow \frac{1}{y}\frac{dy}{dx}=25$
$\Rightarrow \frac{dy}{dx}=25y$
Length of subtangent $=\left|\frac{y}{dy/dx}\right|=\frac{y}{25y}=\frac{1}{25}$