Question

The equation of normal to the curve $x^{\frac{1}{3}}+y^{\frac{1}{3}}=2$ at $(1,1)$ is

• A. $y=2x$
• B. $y=x$
• C. $y=\frac{1}{2}x$
• D. $y=4x$

Answer 1

The correct option is B $y=x$

Given curve:
$x^{\frac{1}{3}}+y^{\frac{1}{3}}=2$
Differentiating w.r.t. $x$,
$\frac{1}{3}{x}^{\frac{-2}{3}}+\frac{1}{3}{y}^{\frac{-2}{3}}{y}^{\prime }=0$
$\Rightarrow$ At $(1,1),y^{\prime }=-1$
Slope of normal $=-\frac{1}{y^{\prime }}=1$
Equation of normal
$\frac{y-1}{x-1}=1\Rightarrow y=x$