Question

All the points on the curve $y^2=4a|x+a\sin \left(x/a\right)|$, where the tangent is parallel to the axis of x are lies on

• A. Circle
• B. Parabola
• C. Straight line
• D. None of these

Answer 1

Answer: (B)

Parabola

$y^2=4a[x+a\sin \left(\frac{x}{a}\right)]$ ..... (i)
$\therefore 2y\frac{dy}{dx}=4a[1+\cos \left(\frac{x}{a}\right)]$ ..... (ii)
If tangent is parallel to x-axis, then
$\frac{dy}{dx}=0$
So, from Eq. (i), we get
$\cos \left(\frac{x}{a}\right)=-1$
$\therefore \sin \left(\frac{x}{a}\right)=0$
On putting this value in Eq. (i), we get
$y^2=4a(x+0)\Rightarrow y^2=4ax$
which is parabola.