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Find the equation of the curve for which the segment of the x-axis intercepted between the origin and the tangent drawn at any point is proportional to the y-coordinate of that point.
- x = y(a - b log y)
- log x = by² + a
- x² = y(a - b log y)
- None of these
Correct answer: x = y(a - b log y)
Solution
X-intercept of tangent = x - y/y'. Condition: x - y/y' = k y. Writing dx/dy - x/y = -k (linear), integrating factor 1/y gives x/y = C - k ln y, so x = y(a - b log y).
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