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If \( P(\theta) \) and \( Q\left(\frac{\pi}{2}+\theta\right) \) are two points on the ellipse
\( \mathrm{P}^{\prime \prime} \)
W \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \), then locus of the mid-point of \( P Q \) is
(1) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\frac{1}{2} \)
(2) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=4 \)
(3) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=2 \)
(4) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\frac{1}{4} \)
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