Question

The equation of the 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 $\frac{x}{a}+\frac{y}{b}=1$

Given equation of curve is

$y=b{e}^{-x/a}$

Let $P(0,y_1)$ be the point where tangent to curve crosses y-axis .

$\Rightarrow y_1=b$

So, the point P is (0,b)

$\frac{dy}{dx}=-\frac{y}{a}$

Slope of tangent at P(0,b) is $-\frac{b}{a}$

Equation of tangent through P(0,b) is

$y-b=-\frac{b}{a}(x-0)$

$\Rightarrow bx+ay=ab$

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