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Question

# The equation x2−2√3xy+3y2−3x+3√3y−4=0 represents.

A
A pair of intersecting lines
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B
A pair of parallel lines with distance between them 52
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C
A pair of parallel lines with distance between them 52
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D
A conic section, which is not a pair of straight lines
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Solution

## The correct option is B A pair of parallel lines with distance between them 52Given equation is x2−2√3xy+3y2−3x+23√3y−4=0We have a=1,h=−√3,g=−32,f=3√32,c=−4Hence, the equation represents a pair of straight lines.Again ah=hb=gf=−1√3Therefore, the lines are parallel. The distance between them=2√g2−aca(a+b)=2  ⎷94+41(1+3)=52Hence, option B is correct.

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