Question

The length of subtangent at any point to the curve $y=b{e}^{-\frac{a}{x}}$ is proportional to -

• A. $x^3$
• B. $y$
• C. $x^2$
• D. $xy$

Answer 1

The correct option is C $x^2$

$y=b{e}^{-\frac{a}{x}}..\left(1\right)$
Differentiating w.r.t $x$ we get,
$\frac{dy}{dx}=b{e}^{-\frac{a}{x}}\frac{a}{x^2}=\frac{ay}{x^2}$ using (1)
Therefore, length of sub tangent is $=\frac{y}{\frac{dy}{dx}}=\frac{x^2}{a}$
Hence, option 'C' is correct.