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.

Prove that the part of the tangent at any point of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 intercepted between the point of contact and the transvers axis is a harmonic mean between the lengths of the perpendiculars drawn from the foci on the normal at the same point.

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.

Find the equation of tangent to the curve y=sin^(-1)(2x)/(1+x^2)a tx=sqrt(3)

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.

Find the point at which the tangent to the curve y=sqrt(4x-3)-1 has its slope (2)/(3) .

Prove that the equation of any tangent to the circle x^2+y^2-2x+4y-4=0 is of the form y=m(x-1)+3sqrt(1+m^2)-2.

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).

Find the equation of the tangent to the curve y= sqrt(3x-2) which is parallel to the line 4x-2y+5=0.

Find the equation of the tangent to the curve (1+x^2)y=2-x , where it crosses the x-axis.

Find the equation of the tangent to the curve (1+x^2)y=2-x , where it crosses the x-axis.