If \[P(\theta )\] and \[Q\left( \frac{\pi }{2}+\theta \right)\] are two points on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then locus of the mid-point of PQ is

\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=4\]

\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=\frac{1}{2},\]

\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=2\]

If \[P(\theta )\] and \[Q\left( \frac{\pi }{2}+\theta \right)\] are tw

1.	If \[P(\theta )\] and \[Q\left( \frac{\pi }{2}+\theta \right)\] are two points on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then locus of the mid-point of PQ is
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
Answer» B. \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=4\]

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If \[P(\theta )\] and \[Q\left( \frac{\pi }{2}+\theta \right)\] are two points on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then locus of the mid-point of PQ is

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