Let \( R S \) be the diameter of the circle \( x^{2}+y^{2}=1 \), wh...

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Let \( R S \) be the diameter of the circle \( x^{2}+y^{2}=1 \), where \( S \) is the point \( (1,0) \). Let \( P \) be a variable point (other than \( R \) and
\( \mathrm{P} \) \( S \) ) on the circle and tangents to the circle at \( S \) and \( P \) meet at

W the point \( Q \). The normal to the circle at \( P \) intersects a line drawn through \( Q \) parallel to \( R S \) at point \( E \). Then the locus of \( E \) passes through the point(s)
(1) \( \left(\frac{1}{3}, \frac{1}{\sqrt{3}}\right) \)
(2) \( \left(\frac{1}{4}, \frac{1}{2}\right) \)
(3) \( \left(\frac{1}{3},-\frac{1}{\sqrt{3}}\right) \)
(4) \( \left(\frac{1}{4},-\frac{1}{2}\right) \)
(JEE Advanced 2016)
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