A) \[\frac{1}{2},\ 9\]
B) \[3,\ \frac{2}{5}\]
C) \[1,\ \frac{2}{3}\]
D) 3, 2
Correct Answer: C
Solution :
Given that, the equation of conic \[9{{x}^{2}}+4{{y}^{2}}-6x+4y+1=0\] Þ\[{{(3x-1)}^{2}}+{{(2y+1)}^{2}}=1\]Þ \[\frac{{{\left( x-\frac{1}{3} \right)}^{2}}}{\frac{1}{9}}+\frac{{{(y+1)}^{2}}}{\frac{1}{2}}=1\]. Here\[a=\frac{1}{3}\], \[b=\frac{1}{2}\]; \ \[2a=\frac{2}{3}\], \[2b=1.\] Length of axes are\[\left( 1,\,\frac{2}{3} \right)\].
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