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A particle moves in the xy-plane along a curve C through the point (3, 3). At any point P on C the tangent meets the x-axis at Q, and the y-axis bisects the segment PQ. Then C is a parabola with:
- length of latus rectum 3
- length of latus rectum 6
- focus (4/3, 0)
- focus (0, 3/4)
Correct answer: length of latus rectum 3
Solution
The condition gives the ODE dy/y = dx/(2x), so y² = 3x through (3,3); this parabola has latus rectum 3 and focus (3/4, 0).
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