Pair Of Straight Lines Question 67

Question: The angle between the pair of straight lines $ x^{2}+4y^{2}-7xy=0 $ , is

[MNR 1983]

Options:

A) $ {{\tan }^{-1}}( \frac{1}{3} ) $

B) $ {{\tan }^{-1}}3 $

C) $ {{\tan }^{-1}}\frac{\sqrt{33}}{5} $

D) $ {{\tan }^{-1}}\frac{5}{\sqrt{33}} $

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Answer:

Correct Answer: C

Solution:

$ \alpha ={{\tan }^{-1}}\frac{2\sqrt{\frac{49}{4}-4}}{5}={{\tan }^{-1}}\frac{\sqrt{33}}{5} $ .