Question

The equation of tangent to the curve $y=b{e}^{-x/a}$ where it cuts the $y$-axis is

• A. $\frac{x}{a}+\frac{y}{b}=1$
• B. $\frac{x}{a}+\frac{y}{b}=-1$
• C. $\frac{x}{a}-\frac{y}{b}=1$
• D. none of these

Answer 1

Answer: (A)

$\frac{x}{a}+\frac{y}{b}=1$

Let the point be $(0,k)$
Substituting this in equation of curve $y=b{e}^{-\frac{x}{a}}$
we get $k=b$ so point is $(0,b)$
Slope $\frac{dy}{dx}=-\frac{b}{a}$
And equation of curve is
$y-b=-\frac{b}{a}(x-0)\frac{x}{a}+\frac{y}{b}=1$