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JEE Advanced 2024 · Paper 1

JEE Advanced 2024 Mathematics question on Circles

Let the straight line y=2xy = 2x touch a circle with center (0,α)(0,\alpha), α>0\alpha > 0, and radius rr at a point A1A_1. Let B1B_1 be the point on the circle such that the line segment A1B1A_1 B_1 is a diameter of the circle. Let α+r=5+5\alpha + r = 5 + \sqrt{5}.

Match each entry in List-I to the correct entry in List-II.
List-I
(P) α\alpha equals
(Q) rr equals
(R) A1A_1 equals
(S) B1B_1 equals
List-II
(1) (−2,4)(-2,4)
(2) 5\sqrt{5}
(3) (−2,6)(-2,6)
(4) 5
(5) (2,4)(2,4)
  1. A.
    (P)→(4)(Q)→(2)(R)→(1)(S)→(3)(P)\to(4)\quad (Q)\to(2)\quad (R)\to(1)\quad (S)\to(3)
  2. B.
    (P)→(2)(Q)→(4)(R)→(1)(S)→(3)(P)\to(2)\quad (Q)\to(4)\quad (R)\to(1)\quad (S)\to(3)
  3. C.
    (P)→(4)(Q)→(2)(R)→(5)(S)→(3)(P)\to(4)\quad (Q)\to(2)\quad (R)\to(5)\quad (S)\to(3)
  4. D.
    (P)→(2)(Q)→(4)(R)→(3)(S)→(5)(P)\to(2)\quad (Q)\to(4)\quad (R)\to(3)\quad (S)\to(5)
Show answer

Correct option: C

[JEE Advanced 2024 · Paper 1]

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