A) \[2{{x}^{2}}-xy-{{y}^{2}}-4x-y=0\]
B) \[2{{x}^{2}}-xy-{{y}^{2}}-4x+y+2=0\]
C) \[2{{x}^{2}}+xy+{{y}^{2}}-2x+y=0\]
D) None of these
Correct Answer: B
Solution :
[b] We have the equation \[2{{x}^{2}}-xy-{{y}^{2}}=0\] \[\Rightarrow (2x+y)(x-y)=0\] If \[(h,k)\] be the point then remaining pair is \[(2x+y+h)(x-y+k)=0\] Where, \[2x+y+h=0\] and \[x-y+k=0\] It passes through the point (1, 0) \[\therefore \,\,\,\,\,\,\,\,2\,\times 1+0+h=\Rightarrow 2+h=0\Rightarrow h=-2\] and \[1-0+k=0\Rightarrow 1+k=0\Rightarrow k=-1\] \[\therefore \] Required pair is \[(2x+y-2)(x-y-1)=0\] \[\Rightarrow 2{{x}^{2}}-2xy-2x+xy-{{y}^{2}}-y-2x+2y+2=0\] \[\therefore \,\,\,\,2{{x}^{2}}-xy-{{y}^{2}}-4x+y+2=0\]
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