The correct option is C an ellipse
13x2−18xy+37y2+2x+14y−2=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+2fgh−af2−bg2−ch2
=(13)(37)(−2)+2(7)(1)(−9)−13(7)2−37(1)2+2(−9)2
=−1600≠0 ⋯(i)
Now, h2−ab=81−481<0 ⋯(ii)
From (i) and (ii),
the above equation represents an ellipse.