The curve for which the ratio of the length of the segment intercepted by any tangent on the Y-axis to the length of the radius vector is constant `(k),` is

Find the curve for which the sum of the lengths of the tangent and subtangent at any of its point is proportional to the product of the co-ordinates of the point of tangency, the proportionality factor is equal to k.

Find the equation of the curve such that the square of the intercept cut off by any tangent from the y-axis is equal to the product of the co-ordinate of the point of tangency.

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.

Find the curve for which the perpendicular from the foot of the ordinate to the tangent is of constant length.

At any point on the curve y=f(x), the length of the sub normal is constant, then the curve is

Find the curve for which the intercept cut off by any tangent on y-axis is proportional to the square of the ordinate of the point of tangency.

A curve is such that the length of the polar radius of any point on the curve is equal to the length of the tangent drawn at this point.Form the differential equation and solve it to find the equation of the curve.

Find the curve for which area of triangle formed by x-axis,tangent drawn at any point on the curve and radius vector of point of tangency is constant,equal to a^(2)

Equation of the line which makes an intercept of length 2 on positive x - axis and an intercept of length 3 on the negative y-axis is