A curve `y=f(x)` has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

A curve passing through the point (1,2) has the property that the perpendicular distance of the origin from normal at any point P of the curve is equal to the distance of P from the x-axis is a circle with radius.

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.

A normal at any point (x , y) to the curve y=f(x) cuts a triangle of unit area with the axis, the differential equation of the curve is

A normal at any point (x,y) to the curve y=f(x) cuts a triangle of unit area with the axis,the differential equation of the curve is

The curve is such that the length of the perpendicular from the origin on the tangent at any point P of the curve is equal to the abscissa of Pdot Prove that the differential equation of the curve is y^2-2x y(dy)/(dx)-x^2=0, and hence find the curve.

The curve is such that the length of the perpendicular from the origin on the tangent at any point P of the curve is equal to the abscissa of Pdot Prove that the differential equation of the curve is y^2-2x y(dy)/(dx)-x^2=0, and hence find the curve.

If the perpendicular distance of a point A, other than the origin from the plane x + y + z = p is equal to the distance of the plane from the origin, then the coordinates of p are