Question

Equation of the curve passing through the point $(a,1)$ and has length of subtangent $=a$ is

• A. $y=e^x$
• B. $y=e^{x/a}$
• C. $y=e^{\frac{x-a}{a}}$
• D. $y=-e^x$

Answer 1

Answer: (C)

$y=e^{\frac{x-a}{a}}$

$y=e^{\frac{x-a}{a}}$ passes through $(a,1)$

Now

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

Length of subtangent=$\begin{array}{c}\left|y\frac{dx}{dy}\right|\\ =\left|e^{\frac{x-a}{a}}\times a{e}^{\frac{x-a}{a}}\right|\\ =\left|a\right|\\ =a\end{array}$

Hence required equation is $y=e^{\frac{x-a}{a}}$