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The parametric equations x = 2 - 3 sec t and y = 1 + 4 tan t describe which of the following curves?
- An ellipse with centre at (2, 1) and eccentricity 3/5
- A circle with centre at (2, 1) and radius 5 units
- A hyperbola with centre at (2, 1) and eccentricity 8/5
- A hyperbola with centre at (2, 1) and eccentricity 5/3
Correct answer: A hyperbola with centre at (2, 1) and eccentricity 5/3
Solution
From x = 2-3sec t, y = 1+4tan t: (x-2)^2/9 - (y-1)^2/16 = 1, a hyperbola centred at (2,1) with a^2=9, b^2=16. Eccentricity e = sqrt(1 + 16/9) = 5/3.
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