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JEE Main202529 Jan 2025Morning ShiftMathematicsCircleActual

Let the line (x+y=1 ) meet the circle (x^2+y^2=4 ) at the points A and B . If the line perpendicular to (A B ) and passing through the mid point of the chord (A B ) intersects the circle at (C ) and (D ), then the area of the quadrilateral ADBC is equal to :

Options

  1. A( 14 )
  2. B(3 7 )
  3. C(2 14 )
  4. D(5 7 )

Correct answer

C. (2 14 )

Step-by-step solution

By solving x = y with circle We get aligned & C ( 2 , 2 ) & D (- 2 ,- 2 ) aligned By solving x + y =1 with circle x^2+y^2=4 we set aligned & A ( 1+ 7 2 , 1- 7 2 ) & & ~B ( 1- 7 2 , 1+ 7 2 ) aligned Area of Quadrilateral ACBD =2 Area of BCD aligned & =2 1 2 | array ccc 2 & 2 & 1 1- 7 2 & 1+ 7 2 & 1 - 2 & - 2 & 1 array | & =2 14 aligned

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