Find the equation of the curve in which the subnormal varies as the square of the ordinate.

Equation of the curve in which the subnormal is thrice the square of the ordinate is given by

Find the curve in which the length of the normal varies as the square of the ordinate.

The equation of the curve whose subnormal is constant is

The equation of the curve whose subnormal is twice the abscissa, is

Prove that for the curve y=be^(x//a) , the subtangent is of constant length and the sub-normal varies as the square of the ordinate .

Show that at any point on the hyperbola xy=c^(2), the subtangent varies as the abscissa and the subnormal varies as the cube of the ordinate of the point of contact.

Find the equation of curves for which the cartesian subtangent varies as the abscissa.

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of and the initial ordinate of the tangent at this point is a constanta =a^(2)