Let RS be the diameter of the circle x2 + y2 = 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)

Engineering

Mathematics

Tangent and Normal to Circle

Question

Let RS be the diameter of the circle x² + y² = 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)

$(\frac{1}{3}, \frac{1}{\sqrt{3}})$

$(\frac{1}{3}, \frac{- 1}{\sqrt{3}})$

$(\frac{1}{4}, \frac{1}{2})$

$(\frac{1}{4}, \frac{- 1}{2})$