Straight Line Question 210
Question: The combined equation of the pair of lines through the point (1, 0) and parallel to the lines represented by $ 2x^{2}-xy-y^{2}=0 $ is
Options:
A) $ 2x^{2}-xy-y^{2}-4x-y=0 $
B) $ 2x^{2}-xy-y^{2}-4x+y+2=0 $
C) $ 2x^{2}+xy+y^{2}-2x+y=0 $
D) None of these
Correct Answer: B $ \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 $ Required pair is $ (2x+y-2)(x-y-1)=0 $ $ \Rightarrow 2x^{2}-2xy-2x+xy-y^{2}-y-2x+2y+2=0 $ $ \therefore 2x^{2}-xy-y^{2}-4x+y+2=0 $
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Answer:
Solution:
$ \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 $
BETA
