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)/(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 slope of the tangent to the curve y=2sqrt2x

The slope of the tangent to the curve x^2+y^2=4 at (sqrt(2),sqrt(2)) is

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 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 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 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.

The tangent at a point P on the curve y =ln ((2+ sqrt(4-x ^(2)))/(2- sqrt(4-x ^(2))))-sqrt(4-x ^(2)) meets the y-axis at T, then PT^(2) equals to :

The tangent at a point P on the curve y =ln ((2+ sqrt(4-x ^(2)))/(2- sqrt(4-x ^(2))))-sqrt(4-x ^(2)) meets the y-axis at T, then PT^(2) equals to :