Mathematics

Mathematics

Problem

Let RSRS be the diameter of the circle x2+y2=1x^2 + y^2 = 1 , where SS is the point (1,0)(1, 0) . Let PP be a variable point (other than RR and SS ) on the circle and tangents to the circle at SS and PP meet at the point QQ . The normal to the circle at PP intersects a line drawn through QQ parallel to RSRS at point EE . Then the locus of EE passes through the point(s) a. (13,13)\left(\frac{1}{3}, \frac{1}{\sqrt{3}}\right) b. (14,12)\left(\frac{1}{4}, \frac{1}{2}\right) c. (13,−13)\left(\frac{1}{3}, -\frac{1}{\sqrt{3}}\right) d. (14,−12)\left(\frac{1}{4}, -\frac{1}{2}\right)

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