A curve is such that the length of perpendicular from origin on the tangent at any point `P` of the curve is equal to the abscissa of `P`. Prove that the differential equation of the curve is `y^2-2xy 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.

There is curve in which the length of the perpendicular from the orgin to tangent at any point is equal to abscissa of that point. Then,

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

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Find the equation of the curve satisfying the above condition and which passes through (1, 1).

If the slope of the tangent is equal to the square of tha abscissa of the point on the curve, then the differential equation is

Find the equation of the curve in which the perpendicular from the origin on any tangent is equal to the abscissa of the point of contact.

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact.Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is

A curve is such that the length of the polar radius of any point on the curve is equal to the length of the tangent drawn at this point.Form the differential equation and solve it to find the equation of the curve.

The length of the perpendicular from the origin,on the normal to the curve, x^(2)+2xy-3y^(2)=0 at the point (2,2) is