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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.\( \left(\frac{1}{4},  -\frac{1}{2}\right)\)

Answer

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Solution

Solution for 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)
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