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Circle question

2016 · Shift 1 · Q28
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  5. /2016 · Shift 1 · Q28

Circle question

2016 · Shift 1 · Q28

JEE AdvancedMathematicsCircleMultiple correct+4 / −2
Let RS be the diameter of the circle x2 + y2=1{x^2}\, + \,{y^2} = 1x2+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)
  1. A
    (13 ,13)\left( {{1 \over 3}\,,{1 \over {\sqrt 3 }}} \right)(31​,3​1​)
  2. B
    (14 ,12)\left( {{1 \over 4}\,,{1 \over 2}} \right)(41​,21​)
  3. C
    (13 ,−13)\left( {{1 \over 3}\,, - {1 \over {\sqrt 3 }}} \right)(31​,−3​1​)
  4. D
    (14 ,−12)\left( {{1 \over 4}\,,-{1 \over 2}} \right)(41​,−21​)
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