Question

The length of subtangent to the curve, $y=e^{\frac{x}{a}}$, is

• A. $2a$
• B. $a$
• C. $\frac{a}{2}$
• D. $\frac{a}{4}$

Answer 1

Answer: (B)

$a$

$y=e^{\frac{x}{a}}$
Let P$(x_1,y_1)$ be any point on the curve.
$y_1=e^{\frac{x_1}{a}}$
$\frac{dy}{dx}=\frac{1}{a}{e}^{\frac{x}{a}}$
Slope of tangent at $(x_1,y_1)=\frac{1}{a}{y}_1$
Length of sub-tangent $=|\frac{y_1}{m}|=a$