Pair Of Straight Lines Question 23
Question: The equation of one of the line represented by the equation $ x^{2}+2xy\cot \theta -y^{2}=0 $ , is
Options:
A) $ x-y\cot \theta =0 $
B) $ x+y\tan \theta =0 $
C) $ x\sin \theta +y(\cos \theta +1)=0 $
D) $ x\cos \theta +y(\sin \theta +1)=0 $
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Answer:
Correct Answer: C
Solution:
The lines represented by the equation $ x^{2}+2xy\cot \theta -y^{2}=0 $ are $ ax+hy\pm y\sqrt{h^{2}-ab}=0 $
$ \Rightarrow x+y\cot \theta \pm y\sqrt{{{\cot }^{2}}\theta +1}=0 $
$ \Rightarrow x+y( \frac{\cos \theta }{\sin \theta }\pm \frac{1}{\sin \theta } )=0 $
$ \Rightarrow x\sin \theta +y(\cos \theta \pm 1)=0 $ Hence, one line is $ x\sin \theta +y(\cos \theta +1)=0 $ .
BETA
