Question

The line $\frac {x} {a} + \frac {y} {b} =1$ touches the curve $y = be^{-x/a}$ at the point

• A. $( a, \frac {b} {a})$
• B. (- a, ba)
• C. $( a, \frac {a} {b})$
• D. none of these

Answer 1

The Correct Option is D

$y = be^{-x/a}$ $\therefore \frac{dy}{dx} = -\frac{b}{a}e^{-x/a}$ Since the line $\frac{x}{a}+\frac{y}{b} = 1$ touches $\left(1\right)$ $\therefore -\frac{1/a}{1/b} = -\frac{b}{a} e^{-x/a}$ i. e., $- \frac{b}{a}= -\frac{b}{a} e^{-x/a}$ $\Rightarrow 1= e^{-x/a}$ $\Rightarrow - \frac{x}{a} = 0$ $\Rightarrow x = 0$ $\therefore y = be^{0} = 0 = b$ Hence reqd. point is $\left(0, b\right)$