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

Prove that all points on the curve y^(2)=4a[x+a sin(x/a)] at which the tangent is parallel to the x-axis lie on a parabola.

Prove that all points on the curve y^(2)=4a[x+a sin((x)/(a))] at which the tangent is parallel to the X - axis lie on the parabola y^(2)=4ax .

Prove that all points of the curve y^2=4a[x+asinx/a] at which the langent is parallel to the axis of x, lie on a parabola.

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.

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

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