A) \[(0,\sqrt{7}),(0,-\sqrt{7})\]
B) \[(0,7),(0,7)\]
C) \[(0,\,2\sqrt{7}),\,(0,\,-2\sqrt{7})\]
D) \[(\sqrt{7},0),(-\sqrt{7},0)\]
E) \[(\sqrt{7},2\sqrt{7}),(\sqrt{7},-2\sqrt{7})\]
Correct Answer: A
Solution :
Since, the foci of the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=1\]are \[(0,\sqrt{7})\]and \[(0,-\sqrt{7})\]. Also, the foci of the ellipse \[\frac{{{x}^{2}}}{9+{{t}^{2}}}+\frac{{{y}^{2}}}{16+{{t}^{2}}}=1\] is\[(0,\sqrt{7})\]and\[(0,-\sqrt{7})\].
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