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 slope of the tangent any point on a curve is lambda times the slope of the joining the point of contact to the origin. Formulate the differential equation and hence find the equation of the curve.

The slope of the tangent any point on a curve is lambda times the slope of the joining the point of contact to the origin. Formulate the differential equation and hence find the equation of the curve.

The slope of the tangent at any point on a curve is lambda times the slope of the line joining the point of contact to the origin. Formulate the differential equation and hence find the equation of the curve.

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

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.

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.

lf length of tangent at any point on th curve y=f(x) intercepted between the point and the x-axis is of length 1. Find the equation of the curve.