The equation of a curve passing through (1,0) for which the product of the abscissa of a point `P` and the intercept made by a normal at `P` on the x-axis equal twice the square of the radius vector of the point `P` is

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

The equation of the curve which passes through the point (2a, a) and for which the sum of the cartesian sub tangent and the abscissa is equal to the constant a , is

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 the curve passing through the point, (5,4) if the sum of reciprocal of the intercepts of the normal drawn at any point P(x,y) on it is 1.

A curve passing through (1,0) is such that the ratio of the square of the intercept cut by any tangent on the y-axis to the Sub-normal is equal to the ratio of the product of the coordinates of the point of tangency to the product of square of the slope of the tangent and the subtangent at the same point,is given by

Find the equation of the curve passing through origin if the slope of the tangent to the cuurve at any point (x,y) is equal to the square of the difference of the abscissa and ordinate of the point.

The curve passing through P(pi^(2),pi) is such that for a tangent drawn to it at a point Q, the ratio of the y - intercept and the ordinate of Q is 1:2 . Then, the equation of the curve is

The abscissa of the point on the curve ay^(2)=x^(3), the normal at which cuts off equal intercepts from the coordinate axes is