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QJEEM21Ma00b9: JEE Main 2021 Mathematics - Class 11 JEEM21Ma00b9 Solution: Let P and Q be two distinct points on a circle which has center …

Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to :

Multiple Choice Options

  • A {(4, 0), (0, 6)}
  • B {(2+22,3−5),(2−22,3+5)}\{ (2 + 2\sqrt 2 ,3 - \sqrt 5 ),(2 - 2\sqrt 2 ,3 + \sqrt 5 )\}
  • C {(2+22,3+5),(2−22,3−5)}\{ (2 + 2\sqrt 2 ,3 + \sqrt 5 ),(2 - 2\sqrt 2 ,3 - \sqrt 5 )\}
  • D {( −- 1, 5), (5, 1)}

Step-by-Step Verified Solution

JEE Main 2021 (Online) 27th July Morning Shift Mathematics - Circle Question 80 English Explanation

tan⁡θ=−23\tan \theta = - {2 \over 3}

Using symmetric from of line

P,Q:(2±13cos⁡θ,3±13sin⁡θ)P,Q:\left( {2 \pm \sqrt {13} \cos \theta ,3 \pm \sqrt {13} \sin \theta } \right)

(2±13.(−313),3±13(213))\left( {2 \pm \sqrt {13} .\left( { - {3 \over {\sqrt {13} }}} \right),3 \pm \sqrt {13} \left( {{2 \over {\sqrt {13} }}} \right)} \right)

( −- 1, 5) & (5, 1)

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