A) \[x-y\cot \theta =0\]
B) \[x+y\tan \theta =0\]
C) \[x\sin \theta +y(\cos \theta +1)=0\]
D) \[x\cos \theta +y(\sin \theta +1)=0\]
Correct Answer: C
Solution :
The lines represented by the equation \[{{x}^{2}}+2xy\cot \theta -{{y}^{2}}=0\]are \[ax+hy\pm y\sqrt{{{h}^{2}}-ab}=0\] \[\Rightarrow x+y\cot \theta \pm y\sqrt{{{\cot }^{2}}\theta +1}=0\] \[\Rightarrow x+y\left( \frac{\cos \theta }{\sin \theta }\pm \frac{1}{\sin \theta } \right)=0\]\[\Rightarrow x\sin \theta +y(\cos \theta \pm 1)=0\] Hence, one line is \[x\sin \theta +y(\cos \theta +1)=0\] .
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