A) \[\frac{{{(x-2)}^{2}}}{3}+\frac{{{(y+3)}^{2}}}{4}=1\]
B) \[\frac{{{(x-2)}^{2}}}{4}+\frac{{{(y+3)}^{2}}}{3}=1\]
C) \[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=1\]
D) None of these
Correct Answer: B
Solution :
Foci \[=(3,-3)\]Þ \[ae=3-2=1\] Vertex \[=(4,-3)\]Þ \[a=4-2=2\]Þ \[e=\frac{1}{2}\] Þ \[b=a\sqrt{\left( 1-\frac{1}{4} \right)}=\frac{2}{2}\sqrt{3}=\sqrt{3}\] Therefore, equation of ellipse with centre \[(2,-3)\]is \[\frac{{{(x-2)}^{2}}}{4}+\frac{{{(y+3)}^{2}}}{3}=1\].
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