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 segment of the tangent to the curve y=a/2I n((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.

Show that the segment of the tangent to the curve y=a/2I n((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.

Show that the segment of the tangent to the curve y=a/2I n((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.

Show that the segment of the tangent to the curve y=a/2I n((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 tangent to curve x=√a^2-y^2 +- a/2 log a-√a^2-y^2 intercepted between curve and x axis is of length

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 axis in constant.

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.