Find the locus of point on the curve `y^2=4a(x+a sin(x/a))` where tangents are parallel to the axis of `x`

All points on the curve y^(2)=4a(x+a" sin"(x)/(a)) at which the tangents are parallel to the axis of x lie on a

The points on the curve y=sin x ,where the tangent is parallel to the x axis is

Find the points on the curve x^(2)+y^(2)-2x-3=0 at which the tangents are parallel to the x-axis.

The number of points on the curve y=x^(3)-2x^(2)+x-2 where tangents are prarllel to x-axis, is

Prove that points of the curve y^(2)=4a{x+a sin((x)/(a))} at which tangents are parallel to x-axis lie on the parabola.

Find the points on the curve 2a^(2)y=x^(3)-3ax^(2), where the tangents are parallel to x -axis.

Find the points on the curve x^2+y^2-2x-3=0 at which the tangents are parallel to the x-axis and y-axis.

Find the coordinates of the point on the curve y^2=3-4x where tangent is parallel to the line 2x+y-2=0 .