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JEE Main 202522 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
22 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Circle

JEE Main 2025 · 22 January · Morning Shift · Mathematics · Circle

A circle C of radius 2 lies in the second quadrant and touches both...

A circle CC of radius 2 lies in the second quadrant and touches both the coordinate axes. Let rr be the radius of a circle that has centre at the point (2,5)(2,5) and intersects the circle CC at exactly two points. If the set of all possible values of r is the interval (α,β)(\alpha, \beta), then 3β−2α3 \beta-2 \alpha is equal to :A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a

Options

  1. A1010
  2. B1515
  3. C1212
  4. D1414

Correct answer

B. 1515

Step-by-step solution

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a C1C2=(2+2)2+(5−2)2=16+9=5r+2>5r>3r<5+2r<7∴α=3,β=73β−2α=3(7)−2(3)=21−6=15\begin{aligned} & C_1 C_2=\sqrt{(2+2)^2+(5-2)^2} \\ & =\sqrt{16+9} \\ & =5 \\ & r+2>5 \\ & r>3 \\ & r < 5+2 \\ & r < 7 \\ & \therefore \alpha=3, \beta=7 \\ & 3 \beta-2 \alpha=3(7)-2(3)=21-6=15\end{aligned}
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