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 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

If the length of the portion of the normal intercepted between a curve and the x-axis varies as the square of the ordinate, find the equation of the curve.

A curve passes through the point (5,3) and the product of its slope and ordinate at any point (x,y) is equal to its abscissa. Find the equation of the curve.

A curve passes through the point (2a,a) and at any point the sum of cartesian subtangent and the abscissa is equal to the constant a. The equation of the curve is

Find the equation of the curve passing through the point (0,1) if the slope of the tangent of the curve at each of it's point is sum of the abscissa and the product of the abscissa and the ordinate of the point.

The slope of the tangent at any arbitrary point of a curve is twice the product of the abscissa and square of the ordinate of the point. Then, the equation of the curve is (where c is an arbitrary constant)

The slope of the tangent at any arbitrary point of a curve is twice the product of the abscissa and square of the ordinate of the point. Then, the equation of the curve is (where c is an arbitrary constant)

The slope of normal at any point P of a curve (lying in the first quadrant) is reciprocal of twice the product of the abscissa and the ordinate of point P. Then, the equation of the curve is (where, c is an arbitrary constant)