jee-advanced 2016 Q49

jee-advanced · India · paper1 Circles Circle-Related Locus Problems
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) $\left(\frac{1}{4}, -\frac{1}{2}\right)$
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) $\left(\frac{1}{4}, -\frac{1}{2}\right)$