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Question

The equation 13x218xy+37y2+2x+14y2=0 represents

A
a pair of straight lines
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B
a circle
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C
an ellipse
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D
a hyperbola
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Solution

The correct option is C an ellipse
13x218xy+37y2+2x+14y2=0
On comparing with ax2+2hxy+by2+2gx+2fy+c=0, we have
a=13, h=9, b=37, g=1, f=7, c=2
Then =abc+2fghaf2bg2ch2
=(13)(37)(2)+2(7)(1)(9)13(7)237(1)2+2(9)2
=16000 (i)

Now, h2ab=81481<0 (ii)
From (i) and (ii),
the above equation represents an ellipse.

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