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 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

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

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.

Prove that the portion of the tangent intercepted,between the point of contact and the directrix of the parabola y^(2)= 4ax subtends a right angle at its focus.

Identify the curve sqrt((x+1)^(2)+y^(2))+ sqrt(x^(2)+(y-1)^(2))-2 =0

lf length of tangent at any point on th curve y=f(x) intercepted between the point and the x-axis is of length 1. Find the equation of the curve.