Question

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

• A. $(a,\frac{b}{a})$
• B. $(-a,\frac{b}{a})$
• C. $(a,\frac{a}{b})$
• D. $None$

Answer 1

The correct option is D $None$

$y=b{e}^{\frac{x}{a}}\therefore \frac{dy}{dx}=-\frac{b}{a}{e}^{\frac{x}{a}}=-\frac{b}{a}(slopeof\frac{x}{a}+\frac{y}{b}=1)\Rightarrow e^{-\frac{x}{a}}=1=e^{\circ }\therefore x=0$
From Eq. (i), y = b
Hence, point (0, b)