A) a pair of straight lines
B) a circle
C) an ellipse
D) a hyperbola
Correct Answer: A
Solution :
The given equation is of the form\[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\], on comparing the given equation with it We obtain\[a=3,\,\,h=\frac{7,}{2},\,\,b=2,\,\,g=\frac{5}{2},\,\,f=\frac{5}{2}\]and\[c=2\] Now,\[abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}\] \[=12+2\times \frac{5}{2}\times \frac{5}{2}\times \frac{7}{2}-3{{\left( \frac{5}{3} \right)}^{2}}-{{\left( \frac{5}{2} \right)}^{2}}-2{{\left( \frac{7}{2} \right)}^{2}}\] \[=0\] Hence, the given equation represents a pair of straight lines.
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