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Circle question

2024 · Shift 1 · Q32
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  1. PYQ Library
  2. /JEE Advanced
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  4. /Circle
  5. /2024 · Shift 1 · Q32

Circle question

2024 · Shift 1 · Q32

JEE AdvancedMathematicsCircleMCQ+3 / −1

Let the straight line y=2xy=2 xy=2x touch a circle with center (0,α),α>0(0, \alpha), \alpha\gt 0(0,α),α>0, and radius rrr at a point A1A_1A1​. Let B1B_1B1​ be the point on the circle such that the line segment A1B1A_1 B_1A1​B1​ is a diameter of the circle. Let α+r=5+5\alpha+r=5+\sqrt{5}α+r=5+5​.

Match each entry in List-I to the correct entry in List-II.

List-I List-II
(P) α\alphaα equals (1) (−2,4)(-2, 4)(−2,4)
(Q) rrr equals (2) 5\sqrt{5}5​
(R) A1A_1A1​ equals (3) (−2,6)(-2, 6)(−2,6)
(S) B1B_1B1​ equals (4) 555
(5) (2,4)(2, 4)(2,4)

The correct option is
  1. A
    (P)→(4)(Q)→(2)(R)→(1)(S)→(3)(\mathrm{P}) \rightarrow(4) \quad(\mathrm{Q}) \rightarrow(2) \quad(\mathrm{R}) \rightarrow(1) \quad(\mathrm{S}) \rightarrow(3)(P)→(4)(Q)→(2)(R)→(1)(S)→(3)
  2. B
    (P)→(2)(Q)→(4)(R)→(1)(S)→(3)(\mathrm{P}) \rightarrow(2) \quad(\mathrm{Q}) \rightarrow(4) \quad(\mathrm{R}) \rightarrow(1) \quad(\mathrm{S}) \rightarrow(3)(P)→(2)(Q)→(4)(R)→(1)(S)→(3)
  3. C
    (P)→(4)(Q)→(2)(R)→(5)(S)→(3)(\mathrm{P}) \rightarrow(4) \quad(\mathrm{Q}) \rightarrow(2) \quad(\mathrm{R}) \rightarrow(5) \quad(\mathrm{S}) \rightarrow(3)(P)→(4)(Q)→(2)(R)→(5)(S)→(3)
  4. D
    (P)→(2)(Q)→(4)(R)→(3)(S)→(5)(\mathrm{P}) \rightarrow(2) \quad(\mathrm{Q}) \rightarrow(4) \quad(\mathrm{R}) \rightarrow(3) \quad(\mathrm{S}) \rightarrow(5)(P)→(2)(Q)→(4)(R)→(3)(S)→(5)
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