A) \[(\pm c,\ \pm c)\]
B) \[(\pm c\sqrt{2},\ \pm c\sqrt{2})\]
C) \[\left( \pm \frac{c}{\sqrt{2}},\ \pm \frac{c}{\sqrt{2}} \right)\]
D) None of these
Correct Answer: B
Solution :
\[xy={{c}^{2}}\]as \[{{c}^{2}}=\frac{{{a}^{2}}}{2}\]. Here, co-ordinates of focus are \[(ae\cos 45{}^\circ ,\,ae\sin 45{}^\circ )\equiv (c\sqrt{2},c\sqrt{2})\],\[\{\because e=\sqrt{2}\],\[a=c\sqrt{2}\}\] Similarly other focus is \[(-c\sqrt{2},-c\sqrt{2})\] Note: Students should remember this question as a fact.
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