All points on the curve y2=4a(x+asinxa)  at which the tangents are parallel to the axis of x , lie on a:

Let P(x1,y1)  be a point of contact. (dydx)(x1,y1)=4a[cos(x1/a)+1]/2y=0 ⇒      cos(x1/a)=−1       ⇒ sin(x1/a)=0 ∴         y12=4a[x1sin(x1/a)]=4ax1 ⇒    Locus of P(x1,y1)  is y2=4ax  which is a parabola.