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.

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.

Find a point M on the curve y=(3)/(sqrt(2))x ln x,x in(e^(-1.5),oo) such that the segment of the tangent at M intercepted between M and the Y-axis is shortest.

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).

A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent is drawn and the on the line y=x. If the curve passes through (1,0), then the curve is

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.

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

A family of curves is such that the length intercepted on the y-axis between the origin and the tangent at a point is three times the ordinate of the point of contact. The family of curves is

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.

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