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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.

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To find the equation of the curve \( y = f(x) \) given that the length of the tangent at any point on the curve intercepted between the point and the x-axis is of length 1, we can follow these steps: ### Step 1: Understand the Geometry Let \( P(x, y) \) be a point on the curve. The tangent at point \( P \) intersects the x-axis at point \( Q(X, 0) \). The length of the segment \( PQ \) is given to be 1 unit. ### Step 2: Equation of the Tangent The equation of the tangent line at point \( P \) can be expressed as: \[ ...
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