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.

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 .

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 equation of the curve which is such that the portion of the axis of x cut off between the origin and tangent at any point is proportional to the ordinate of that point is

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.

Find the points on the curve y=4x^3-3x+5 at which the equation of the tangent is parallel to the X-axis.

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 such that the portion of the x-axis cut off between the origin and the tangent at a point is twice the abscissa and which passes through the point (1,2).

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find all the curves y=f(x) such that the length of tangent intercepted between the point of contact and the x-axis is unity.