Verified Solution • 2025–26 Session moderate

QJEEM21Mabd57: JEE Main 2021 Mathematics - Class 11 JEEM21Mabd57 Solution: A circle C touches the line x = 2y at the point (2, 1) and…

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle

C1 : x2 + y2 + 2y −- 5 = 0 at two points P and Q such that PQ is a diameter of C1. Then the diameter of C is :

Multiple Choice Options

  • A 757\sqrt 5
  • B 15
  • C 285\sqrt {285}
  • D 4154\sqrt {15}

Step-by-Step Verified Solution

(x −- 2)2 + (y −- 1)2 + λ\lambda (x −- 2y) = 0

C : x2 + y2 + x( λ\lambda −- 4) + y( −- 2 −- 2 λ\lambda ) + 5 = 0

C1 : x2 + y2 + 2y −- 5 = 0

S1 −- S2 = 0 (Equation of PQ)

( λ\lambda −- 4)x −- (2 λ\lambda + 4)y + 10 = 0 Passes through (0, −- 1)

⇒\Rightarrow λ\lambda = −- 7

C : x2 + y2 −- 11x + 12y + 5 = 0

= 2454{{\sqrt {245} } \over 4}

Diameter = 757\sqrt 5

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