Question

The curve represented by x = a(cos hθ + sin hθ), y = b (cos hθ - sin hθ) is

• A. A hyperbola
• B. An ellipse
• C. A parabola
• D. A circle

Answer 1

Answer: (A)

A hyperbola

Answer 2

We have, x = a (cosh θ + sinh θ),

y = b (cosh θ - sinh θ)

⇒ $\frac{x}{a}.\frac{y}{b} = {\cos h}^{2}\theta - {\sin h}^{2}\theta = 1$

⇒ xy = ab, which is a hyperbola.