Question

if normal to the curve $y=f\left(x\right)$is parallel to $x$-axis then correct statement is

• A. $\frac{dy}{dx}=0$
• B. $\frac{dy}{dx}=1$
• C. $\frac{dx}{dy}=0$
• D. None of these

Answer 1

The correct option is C

$\frac{dx}{dy}=0$

Explanation for correct option

The slope of the normal is $\frac{-1}{{\displaystyle \frac{dy}{dx}}}$.

It is parallel to the $x$−axis.

$\Rightarrow \frac{-1}{{\displaystyle \frac{dy}{dx}}}=0$

$\Rightarrow \frac{dx}{dy}=0$

Hence, option C is correct.