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Find the combined equation of the pair o...

Find the combined equation of the pair of lines through the point (1, 0) and parallel to the lines represented by `2x^2-x y-y^2=0`

Text Solution

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The correct Answer is:
`2x^(2)-xy-y^(2)-4x+y+2=0`.
The given pair of lines is `(2x+y)(x-y)=0`. So , the required pair of lines is
`(2x+y+k)(x-y+k')=0` were `2x+y+k=0and x-y+k'=0` pass through (1,0). Therefore ,
`k=-2,k=-1`
therefore , the required pair of lines is
`(2x+y-2)(x-y-1)=0`
or `2x^(2)-y^(2)-xy-4x+y+2=0`
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