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How many common tangents of finite (non-zero) slope exist for the curves xy = c² and y² = 4ax?

1. 1
2. 0
3. 2
4. 4

Correct answer: 1

Solution

Imposing tangency of y = mx + a/m to xy = c² leads to m³ = -a/(4c²) form, giving exactly one real value of m, hence one common tangent of finite slope.

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