Question

The equation of tangent to the curve $y=b{e}^{(-x/a)}$ at the point where it crosses the $y-$ axis is

• A. $\frac{x}{a}-\frac{y}{b}=1$
• B. $ax+by=1$
• C. $ax-by=1$
• D. $\frac{x}{a}+\frac{y}{b}=1$

Answer 1

The correct option is D $\frac{x}{a}+\frac{y}{b}=1$

$y=b{e}^{(-x/a)}$ meets the $y-$ axis at $(0,b)$
$\frac{dy}{dx}=b{e}^{(-x/a)}\left(\frac{-1}{a}\right)$
$(\frac{dy}{dx}{)}_{(0,b)}=b{e}^0\left(\frac{-1}{a}\right)=\frac{-b}{a}$
$\therefore$ required tangent is $y-b=\frac{-b}{a}(x-0)$ or $\frac{x}{a}+\frac{y}{b}=1$