Question

Co-ordinates of a point on the curve y=x log x at which the normal is parallel to the line 2x -2y =3 are

• A. (0,0)
• B. (e,e)
• C. $(e^2,2e^2)$
• D. $(e^{-2},-2e^{-2})$

Answer 1

The correct option is D $(e^{-2},-2e^{-2})$

$y=xlogx\Rightarrow \frac{dy}{dx}=1+logx$
The slope of the normal = $-\frac{1}{\left(\frac{dy}{dx}\right)}=\frac{-1}{1+logx}$
The slope of the line 2x -2y=3 is 1.
$\therefore \frac{-1}{1+logx}=1\Rightarrow logx=-2\Rightarrow x=e^{-2}\therefore y=-2e^{-2}$
$\therefore$ Co-ordinate of the point is $(e^{-2},-2e^{-2})$.