A) circle
B) parabola
C) ellipse
D) hyperbola
Correct Answer: B
Solution :
Given equation is \[{{x}^{2}}+{{y}^{2}}-2x{{y}^{4}}-20x+10=0\] On comparing the given equation with \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0,\]we get \[a=1,\text{ }h=-1,\text{ }b=1,\text{ }g=10,\,f=0,\text{ }c=10\] Now, \[\Delta =abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}\] \[=10+0-0-100-10\ne 0\] And \[{{h}^{2}}-ab=1-1=0\] Since, \[\Delta \ne 0\] and \[{{h}^{2}}-ab=0\] Therefore, given equation represents a parabola.
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