A curve passing through the origin, is such that the middle point of the segment of normal between point of contact and x axis lies on the parabola `2y^2=x`, then equation of curve is

A curve passing through the origin is such that the middle point of the segment of normal between point of contact and x-axis lies on the parabola 2y^(2)=x, then the equation of curve is

Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola 2y^2=x .

Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola 2y^2=x .

Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x- axis lies on the parabola 2y^(2)=x

Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola 2y^2=x

Find the equation of a curve passing through the point (1, 1) , given that the segment of any tangent drawn to the curve between the point of tangency and the y-axis is bisected at the x-axis.

Find the equation of the curve passing through the origin.given that the slope of tangent to the curve at any point point is y+2x.

At any point P(x,y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact P to the point (-4,-3) Find the equation of the curve given that it passes through the point (-2, 1)

A curve C passes through origin and has the property that at each point (x,y) on it the normal line at that point passes through (1,0) The equation of a common tangent to the curve C and the parabola y^(2)=4x is