Question

The equation of the normal to the curve $ y = e^x $ at $(0,1)$ is

• A. 2x + y = 1
• B. y - x = 1
• C. x + y = 1
• D. None of these

Answer 1

Answer: (C)

Given curve is $y=e^{x} \Rightarrow \frac{d y}{d x}=e^{x}$
Slope of normal $=\frac{-1}{e^{x}}$
$\therefore$ Slope of normal at point $(0,1)=\frac{-1}{e^{0}}=-1$
The equation of normal at $(0,1)$ is given by
$ (y-1)=-1(x-0) $
$\Rightarrow x+y=1$