A) parabola
B) ellipse
C) hyperbola
D) none of these
Correct Answer: C
Solution :
We have \[13[{{(x-1)}^{2}}+{{(y-2)}^{2}}]=3{{(2x+3y-2)}^{2}}\] \[\Rightarrow \]\[13({{x}^{2}}+{{1}^{2}}-2x+{{y}^{2}}+4-4y)\] \[=3(4{{x}^{2}}+9{{y}^{2}}+4+12xy-12y-8x)\] \[\Rightarrow \]\[{{x}^{2}}-14{{y}^{2}}-2x-16y+53-36xy=0\] Here, coefficient of \[{{x}^{2}}\]and \[{{y}^{2}}\]is in opposite sign and \[\Delta \ne 0.\] \[\therefore \] It represents a hyperbola.
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