Question

7. Prove that all points of the curve y2 = 4a { x + a sin (x/a)} at
which the tangent is parallel to the X-axis lie on a parabola.
[ C.P. 1998]​

Answer 1

Answer:

y2=4a[x+asin(ax​)] ... (i)

∴2ydxdy​=4a[1+cos(ax​)] ... (ii)

If tangent is parallel to x-axis, then

dxdy​=0

So, from Eq. (i), we get

cos(ax​)=−1

∴sin(ax​)=0

On putting this value in Eq. (i), we get

y2=4a(x+0)⇒y2=4ax

which is parabola.

Step-by-step explanation: