Question

Angle between the lines represented by the equation $x^{2} + 2xy\sec\theta + y^{2} = 0$ is

• A. $\theta$
• B. $2\theta$
• C. $\frac{\theta}{2}$
• D. None of these

Answer 1

Answer: (A)

$\theta$

Answer 2

Let angle between both the lines is $\alpha$, then

$\alpha = \tan^{- 1}\left( \frac{2\sqrt{h^{2} - ab}}{a + b} \right) = \tan^{- 1}\left( \frac{2\sqrt{\sec^{2}\theta - 1}}{1 + 1} \right) = \theta$ .