Question

For the hyperbola x²sec²a–y²cosec²a = 1 which of the

following remains constant with the changes of a.

• A. Abscissa of vertices
• B. Abscissa of foci
• C. Eccentricity
• D. Directrices

Answer 1

Answer: (B)

Abscissa of foci

Answer 2

Equation of hyperbola is $\frac{x^{2}}{\cos^{2}\alpha} - \frac{y^{2}}{\sin^{2}\alpha} = 1$

a² = cos² a & b² = sin² a Ž a² + b² = 1 …..(1)

Q b² = a² (e² –1)

Ž b² = a²e² –a² Ž a² +b² = a²e²

Ž a²e² = 1 (fron (1))

Hence abscissa of foci is independent of a