Question

Angle between the asymptotes of the hyperbola

x² + 2xy – 3y² + x + 7y + 9 = 0 is –

• A. tan^–1 (± 2)
• B. tan^–1 (±$\sqrt{3}$)
• C. tan^–1$\left( \frac{1}{\sqrt{3}} \right)$
• D. tan^–1$\left( \frac{1}{2} \right)$

Answer 1

Answer: (A)

tan^–1 (± 2)

Answer 2

Equation of asymptotes of the hyperbola are x² + 2xy – 3y² = 0

The angle between asymptotes is

q = tan^–1 $\left( \frac{1 - 1( - 3)}{1 - 3} \right)$

= tan^–1 $\left( \frac{1 + 3}{- 2} \right)$

= tan^–1 (±2).