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JEE Main 20245 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Circle

JEE Main 2024 · 5 April · Morning Shift · Mathematics · Circle

Let a circle C of radius 1 and closer to the origin be such that...

Let a circle CC of radius 1 and closer to the origin be such that the lines passing through the point (3,2)(3,2) and parallel to the coordinate axes touch it. Then the shortest distance of the circle C\mathrm{C} from the point (5,5)(5,5) is :Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3,2) and parallel

Options

  1. A222 \sqrt{2}
  2. B424 \sqrt{2}
  3. C4
  4. D5

Correct answer

C. 4

Step-by-step solution

Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3,2) and parallel
Coordinates of the centre will be (2,1)(2,1) Equation of circle will be (x−2)2+(y−1)2=1QC=(5−2)2+(5−1)2QC=5\begin{aligned} & (\mathrm{x}-2)^2+(\mathrm{y}-1)^2=1 \\ & \mathrm{QC}=\sqrt{(5-2)^2+(5-1)^2} \\ & \mathrm{QC}=5 \end{aligned} shortest distance =RQ=CQ−CR=5−1=4\begin{aligned} & =\mathrm{RQ}=\mathrm{CQ}-\mathrm{CR} \\ & =5-1 \\ & =4 \end{aligned}
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