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Question

The conic represented by the equation x2+y22xy+20x+10=0 is

A
a parabola
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B
an ellipse
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C
a hyperbola
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D
a pair fo straight line
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Solution

The correct option is A a parabola
On compairing the given eqaution with the equation
ax2+by2+2hxy+2gx+2fy+c=0 we get
a=b=1,h=1,c=10,g=10 and f=0
Δ=abc+2fghaf2bg2ch2=1010010=1000
and h2=1=ab
Hence given equation represents a parabola

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