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Find the curve passing through (2, 3) such that the part of every tangent line intercepted between the coordinate axes is bisected at the point where it touches the curve.

1. (x/2)² + (y/3)² = 2
2. 2y - 3x = 0
3. y = 6/x
4. x² + y² = 13

Correct answer: y = 6/x

Solution

The bisection condition forces dy/dx = -y/x, whose solution is xy = c; through (2,3), c = 6, so xy = 6, i.e. y = 6/x.

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