What is the Cartesian equation of the hyperbola with parametric equations x = 3sec(t) and y = 4tan(t)?
Answer and explanation
Correct answer: A. x^2 / 9 - y^2 / 16 = 1
- Step 1: From the parameters: sec(t) = x / 3 and tan(t) = y / 4. Step 2. Identity: sec^2(t) - tan^2(t) = 1. Substitute: (x/3)^2 - (y/4)^2 = 1 => x^2 / 9 - y^2 / 16 = 1. Answer: x^2 / 9 - y^2 / 16 = 1. Why not the others: Eliminating the parameter yields a standard horizontal hyperbola.
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