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If the \( \Large \angle \theta \) is acute, then the acute angle between \( \Large x^{2} \left(\cos \theta -\sin \theta \right)+2xy \cos \theta +y^{2} \left(\cos \theta +\sin \theta \right)=0 \) is


A) \( \Large 2 \theta \)

B) \( \Large \frac{ \theta }{3} \)

C) \( \Large \theta \)

D) \( \Large \frac{ \theta }{2} \)

Correct Answer:
C) \( \Large \theta \)

Description for Correct answer:
Comparing the given equation, we get

\( \Large a=\cos \theta - \sin \theta ,\ b=\cos \theta + \sin \theta ,\ h=\cos \theta \)

\( \Large tan\phi =\frac{2\sqrt{h^{2}-ab}}{a+b} \)

=>\( \Large \tan \phi = \frac{2\sqrt{\cos^{2} \theta - \left(\cos^{2} \theta - \sin^{2} \theta \right) }}{\cos \theta - \sin \theta +\cos \theta +\sin \theta } = \frac{2\sin \theta }{2\cos \theta } \)

=> \( \Large \tan \phi = \tan \theta => \phi = 0 \)

Part of solved Straight lines questions and answers : >> Elementary Mathematics >> Straight lines




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