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 slope of the tangent to the curve y=2sqrt2x

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.

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 lenght of the portion of the tangent to the curve x^(2/3)+y^(2/3)=a^(2/3) at any point of it, intercept between the coordinate axes is contant.

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

The parametric equation of a curve is given by, x=a(cos t+log tan(t/2)) , y=a sin t. Prove that the portion of its tangent between the point of contact and the x-axis is of constant length.

If length of tangent at any point on the 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.