Let RS 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 S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point(s)
A.\( \left(\frac{1}{3}, \frac{1}{\sqrt{3}}\right)\)
B.\( \left(\frac{1}{4}, \frac{1}{2}\right)\)
C.\( \left(\frac{1}{3}, -\frac{1}{\sqrt{3}}\right)\)
D.\( \left(\frac{1}{4}, -\frac{1}{2}\right)\)