A) \[{{x}^{2}}-\sqrt{3}xy=0\]
B) \[xy-\sqrt{3}{{y}^{2}}=0\]
C) \[\sqrt{3}{{x}^{2}}-xy=0\]
D) None of the above
Correct Answer: C
Solution :
The given equation of pair of straight lines can be rewritten as\[(\sqrt{3}x-y)(x-\sqrt{3}y)=0\]. Their separate equations are, \[y=\sqrt{3}x\]and\[y=\frac{1}{\sqrt{3}}x\] \[\Rightarrow \] \[y=\tan {{60}^{o}}x\] and\[y=\tan {{30}^{o}}x\] After rotation, the separate equations are \[y=\tan {{90}^{o}}x\] and \[y=\tan {{60}^{o}}x\] \[\Rightarrow \] \[x=0\]and\[y=\sqrt{3}\cdot x\] \[\therefore \]Combined equation in the new position is \[x(\sqrt{3}x-y)=0\]or\[\sqrt{3}{{x}^{2}}-xy=0\]
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