A) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=\frac{1}{2},\]
B) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=4\]
C) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=2\]
D) None of these
Correct Answer: A
Solution :
[a] Clearly P is \[(acos\theta ,bsin\theta )\]and Q is \[(-asin\theta ,b\sin \theta )\] so the midpoint (h, k) or PQ will be given by \[h=\frac{a\cos \theta -a\sin \theta }{2}\] And \[k=\frac{b\sin \theta +b\cos \theta }{2}\] \[\therefore \frac{4{{h}^{2}}}{{{a}^{2}}}+\frac{4{{k}^{2}}}{{{b}^{2}}}=2\Rightarrow \frac{{{h}^{2}}}{{{a}^{2}}}+\frac{{{k}^{2}}}{{{b}^{2}}}=\frac{1}{2}\]You need to login to perform this action.
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