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From a point \( P \) perpendicular tangents \( P Q \) and \( P R \)
\( \mathrm{P} \) are drawn to ellipse \( x^{2}+4 y^{2}=4 \), then locus of

W circumcenter of triangle \( P Q R \) is
(1) \( x^{2}+y^{2}=\frac{16}{5}\left(x^{2}+4 y^{2}\right)^{2} \)
(2) \( x^{2}+y^{2}=\frac{5}{16}\left(x^{2}+4 y^{2}\right)^{2} \)
(3) \( x^{2}+4 y^{2}=\frac{16}{5}\left(x^{2}+y^{2}\right)^{2} \)
(4) \( x^{2}+4 y^{2}=\frac{16}{5}\left(x^{2}+y^{2}\right)^{2} \)
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