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JEE Advanced2024MathematicsCircleActual

Let the straight line y =2 x touch a circle with center (0, ), >0 , and radius r at a point A ₁ . Let B ₁ be the point on the circle such that the line segment A₁ B₁ is a diameter of the circle. Let +r=5+ 5 . Match each entry in List-I to the correct entry in List-II. The correct option is

Options

  1. A( P ) (4) ( Q ) (2) ( R ) (1) ( S ) (3)
  2. B( P ) (2) ( Q ) (4) ( R ) (1) ( S ) (3)
  3. C( P ) (4) ( Q ) (2) ( R ) (5) ( S ) (3)
  4. D( P ) (2) ( Q ) (4) ( R ) (3) ( S ) (5)

Correct answer

C. ( P ) (4) ( Q ) (2) ( R ) (5) ( S ) (3)

Step-by-step solution

Consider centre as P (0, ), >0 | 2(0)- 5 |=r aligned & |- |= 5 r & = 5 r & +r=5+ 5 & 5 r+r= 5 ( 5 +1) & r= 5 , =5 & P(0,5) aligned Foot of perpendicular from P to line 2 x - y =0 aligned & x-0 2 = y-5 -1 = -(2(0)-5) 5 =1 & x=2, y=4 A₁(2,4) aligned Let B ( p , q ) p +2 2 =0, q +4 2 =5 p =-2, q =6 ~B (-2,6)

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