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Does equation x^2+2y^2-2sqrt(3)x-4y+5=0 ...

Does equation `x^2+2y^2-2sqrt(3)x-4y+5=0` satisfies the condition `a b c+2gh-af^2-bg^2-c h^2=0?` Does it represent a pair of straight lines?

Text Solution

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Given equation is `x^(2)+2y^(2)-2sqrt(3)x-4y+5=0`.
Here , `a=1,b=2,h=0,g=-sqrt(3),f=-2,c=5`. But , `abc+2gh-af^(2)-bg^(2)-ch^(2)=10+0-4-6=0`.
The given equation can written as
`(x-sqrt(3))^(2)+2(y-1)^(2)=0`
Hence , it denotes only a point `P(sqrt(3),1)` but not a pair of straight lines .
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