Question

If tangent to curve at a point is perpendicular to $x$ - axis then at that point -

• A. $\frac{dy}{dx}=0$
• B. $\frac{dx}{dy}=0$
• C. $\frac{dy}{dx}=1$
• D. $\frac{dy}{dx}=-1$

Answer 1

Answer: (B)

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

We know slope of tangent to the any curve ${}^{\prime }{y}^{\prime }$ is $m=\frac{dy}{dx}$
Now if line is perpendicular to x-axis this means its slope is $\infty$
$\Rightarrow \frac{dy}{dx}\to \infty \Rightarrow \frac{dx}{dy}=0$
Hence, option 'C' is correct.