Question

The angle between the pair of straight lines represented by $2x^{2} - 7xy + 3y^{2} = 0$is

• A. $60^{o}$
• B. $45^{o}$
• C. $\tan^{- 1}(7/6)$
• D. $30^{o}$

Answer 1

Answer: (B)

$45^{o}$

Answer 2

Angle between the lines is ,

$\theta = \tan^{- 1}\left| \frac{2\sqrt{h^{2} - ab}}{a + b} \right| = \tan^{- 1}\left| \frac{2\sqrt{\left( - \frac{7}{2} \right)^{2} - (2)(3)}}{2 + 3} \right|$

⇒ $\theta = \tan^{- 1}\left( \frac{2}{5}.\frac{5}{2} \right) = \tan^{- 1}(1)$ ⇒ $\theta = 45^{o}$