Length of subtangent is defined as the length of projection of tangent between the points where the tangent is drawn and the point where the tangent meets x-axis.

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Length of subtangent is defined as the perpendicular distance between the point where the tangent is drawn and x-axis

[PT = length of tangent, $(x_{1}, y_{1})$ is the point where the tangent is drawn, is the angle the tangent makes with x-axis, $x_{1}, y_{1}$ , PT > 0]

How many of the following gives the length of subtangent ?

Which of the following gives the length of subtangent ?

[PT = length of tangent, (x1,y1) is the point where the tangent is drawn, $θ$ is the angle the tangent makes with x-axis, x1, y1, PT > 0]

Find the length of subtangent on the curve $y = \frac{x}{1 + x}$ , where the slope of the tangent is $\frac{1}{9}$

[ The point where the tangent is drawn is in first quadrant ]

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