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.given that the slope of tangent to the curve at any point point is y+2x.

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 point (1,1) , given that the slope of the tangent to the curve at any point is (x)/( y)

Find the equation of the curve passing through the point (1,1) , given that the slope of the tangent to the curve at any point is (2y)/( x)

Find the equation of the curve passing through the point (1,0) if the slope of the tangent to the curve at any point (x,y)is(y-1)/(x^(2)+x)

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x,y) is equal to the sum of the coordinates of the point.

Find the equation of a curve passing through the point (1.1) if the perpendicular distance of the origin from the normal at any point P(x,y) of the curve is equal to the distance of P from the x-axis.

Find the equation of a curve passing through the point (1.1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.

Find the equation of a curve passing through the point (1.1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.

Find the equation of a curve passing through the origin, given that the slope of the tangent of the curve at any point (x,y) is equal to tha sum of the coordinates of the point.