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.

Prove that the portion of the tangent to the curve (x+sqrt(a^2-y^2))/a=(log)_e(a+sqrt(a^2-y^2))/y intercepted between the point of contact and the x-axis is constant.

Show that the length of the tangent to the parabola y^2 = 4ax intercepted between its point of contact and the axis of the parabola is bisected by the tangent at the vertex.

In the curve x= a (cos t+ log tan(t/2)) , y =a sin t . Show that the portion of the tangent between the point of contact and the x-axis is of constant length.

In the curve x= a (cos t+ log tan(t/2)) , y =a sin t . Show that the portion of the tangent between the point of contact and the x-axis is of constant length.

Find the equation of a curve passing through the point (1, 1) , given that the segment of any tangent drawn to the curve between the point of tangency and the y-axis is bisected at the x-axis.

Find a point M on the curve y=3/(sqrt(2))\ \ xlnx ,\ x\ in (e^(-1. 5),\ oo) such that the segment of the tangent at M intercepted between M and the Y-axis is shortest.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

In the curve x^a y^b=K^(a+b) , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).

In the curve x^a y^b=K^(a+b) , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).