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Question

The conic represented by the equation 13x2−18xy+37y2+2x+14y−2=0 is

A
a circle
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B
an ellipse
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C
a parabola
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D
a hyperbola
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Solution

The correct option is B an ellipse
On comparing the given equation with the equation ax2+2hxy+by2+2gx+2fy+c=0
we get,
a=13,b=37,c=2,f=7,g=1, and h=9
=abc+2fghaf2bg2ch2
=96212663737+1620
and h2ab=8113×37<0
Thus, we have
0 and h2<ab.
So, the given equation represents an ellipse.

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