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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.
- (x/2)² + (y/3)² = 2
- 2y - 3x = 0
- y = 6/x
- 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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