Question

Length of the subtangent to the curve $y=e^{\frac{x}{a}}$ is:

• A. $e^{\frac{x}{a}}$
• B. $a$
• C. $\frac{2}{a}$
• D. None of these

Answer 1

The correct option is B $a$

Subtangent is given by $\frac{y}{\frac{dy}{dx}}$

Here, $y=e^{\frac{x}{a}}$

$\frac{dy}{dx}=\frac{1}{a}\times e^{\frac{x}{a}}$

$\Rightarrow$ Subtangent $=\frac{y}{\frac{dy}{dx}}=\frac{e^{\frac{x}{a}}}{\frac{1}{a}\times e^{\frac{x}{a}}}=a$