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

The equation of the curve lying in the first quadrant, such that the portion of the x - axis cut - off between the origin and the tangent at any point P is equal to the ordinate of P, is (where, c is an arbitrary constant)

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

The curve such that the intercept on the X-axis cut-off between the origin, and the tangent at a point is twice the abscissa and passes through the point (2, 3) is

The equation of the curve such that the distance between the origin and the tangent at an arbitrary point is equal to the distance between the origin and the normal at the same point is

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

The equation of curve in which portion of y- axis cutoff between origin and tangent varies as cube of abscissa of point of contact is

The equation of the curve in which the portion of the tangent included between the coordinate axes is bisected at the point of contact, is

A curve is such that the intercept 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). If the ordinate of the point on the curve is 1/3 then the value of abscissa is :