A) \[12{{x}^{2}}-4{{y}^{2}}-24x+32y-127=0\]
B) \[12{{x}^{2}}+4{{y}^{2}}+24x-32y-127=0\]
C) \[12{{x}^{2}}-4{{y}^{2}}-24x-32y+127=0\]
D) \[12{{x}^{2}}-4{{y}^{2}}+24x+32y+127=0\]
Correct Answer: A
Solution :
Foci are (6,4) and (?4,4), \[e=2\]and centre is \[\left( \frac{6-4}{2},4 \right)=(1,4)\] Þ\[6=1+ae\]Þ \[ae=5\]Þ \[a=\frac{5}{2}\]and \[b=\frac{5}{2}(\sqrt{3})\] Hence the required equation is \[\frac{{{(x-1)}^{2}}}{(25/4)}-\frac{{{(y-4)}^{2}}}{(75/4)}=1\] or \[12{{x}^{2}}-4{{y}^{2}}-24x+32y-127=0\].
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