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JEE Main202127 Jul 2021Morning ShiftMathematicsCircleActual

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 O C is perpendicular to both the line segments C P and C Q , then the set P , Q is equal to

Options

  1. A4 , 0 , 0 , 6
  2. B2 + 2 2 , 3 - 5 , 2 - 2 2 , 3 + 5
  3. C2 + 2 2 , 3 + 5 , 2 - 2 2 , 3 - 5
  4. D- 1 , 5 , 5 , 1

Correct answer

D. - 1 , 5 , 5 , 1

Step-by-step solution

Given the circle has centre 2 , 3 and it passes through the point 0 , 0 . So, the radius of the circle is 2 2 + 3 2 = 13 The equation of the line which passes through the point 0 , 0   &   2 , 3 is y - 0 = 3 - 0 2 - 0 x - 0 ⇒ y = 3 2 x So, the slope of O C = 3 2 From the diagram, the line P Q is perpendicular to the line O C . So, the slope of P Q is - 2 3 So, tan θ = - 2 3 Using symmetric from of line The coordinate of P = 2 + 13 cos θ , 3 + 13 sin θ = 2 + 13 · - 3 13 , 3 +

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