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.

Find the equation of the curve passing through the point (0, -2) given that at any point (x , y) on the curve the product of the slope of its tangent and y coordinate of the point is equal to the x-coordinate of the point.

Show that the equation of the curve passing through the point (2,1) and for which the sum of the subtangent and the abscissa is equal to 1 is y(x-1)=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

A curve passes through (2, 1) and is such that the square of the ordinate is twice the rectangle contained by the abscissa and the intercept of the normal. Then the equation of curve is

The Curve possessing the property that the intercept made by the tangent at any point of the curve on they-axis is equal to square of the abscissa of the point of tangency, is given by

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