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Which of the following parametric forms (with parameter t) represents a hyperbola?

1. all of these
2. x = (a/2)(t + 1/t) and y = (b/2)(t - 1/t)
3. x = e^t + e^(-t) and y = e^t - e^(-t)
4. x² - 6 = 2 cos t and y² + 2 = 4 cos²(t/2)

Correct answer: all of these

Solution

Each parametrization eliminates to a difference-of-squares = constant (hyperbola), so all of them represent hyperbolic profiles.

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