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[" 18.Prove that the segment of the tang...

[" 18.Prove that the segment of the tangent to the curve "],[y=(a)/(2)log(a+sqrt(a^(2)-x^(2)))/(a-sqrt(a^(2)-x^(2)))-sqrt(a^(2)-x^(2))],[" contained between the point of contact and the "],[" "u-axis has a constant length."]

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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

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.

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.

y=log[(x+sqrt(x^(2)+a^(2)))/(sqrt(x^(2)+a^(2))-x)]

y = log((sqrt(x^(2)+a^(2))+x)/(sqrt(x^(2)+a^(2))-x))

y = log((sqrt(x^(2)+a^(2))+x)/(sqrt(x^(2)+a^(2))-x))