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 portion of the tangent to the curve x=sqrt(a^(2)-y^(2))+(a)/(2)(log(a-sqrt(a^(2)-y^(2))))/(a+sqrt(a^(2)-y^(2))) intercepted between the curve and x -axis,is of legth.

Show that the length of the portion of the tangent to the curve x^((2)/(3))+y^((2)/(3))=4 at any point on it,intercepted between the coordinate axes is constant.

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 segment of the tangent to the curve y=(a)/(2)In((a+sqrt(a^(2)-x^(2)))/(a-sqrt(a^(2)-x^(2))))-sqrt(a^(2)-x^(2)) contained between the y= axis and the point of tangency has a constant length.

The portion of the tangent of the curve x^(2/3)+y^(2/3)=a^(2/3) ,which is intercepted between the axes is (a>0)

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 the tangent to the curve sqrt(x)+sqrt(y)=a at the point ((a^(2))/(4),(a^(2))/(4))