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JEE Main 202118 MarchMorning Shift
Exam
JEE Main
Year
2021
Date
18 March
Shift
Morning Shift
Subject
Mathematics
Chapter
Circle

JEE Main 2021 · 18 March · Morning Shift · Mathematics · Circle

Choose the correct statement about two circles whose equations are...

Choose the correct statement about two circles whose equations are given below:

x2+y2−10x−10y+41=0{x}^{2} + {y}^{2} - 10x - 10y + 41 = 0

x2+y2−22x−10y+137=0{x}^{2} + {y}^{2} - 22x - 10y + 137 = 0

Options

  1. Acircles have same centre
  2. Bcircles have no meeting point
  3. Ccircles have only one meeting point
  4. Dcircles have two meeting points

Correct answer

C. circles have only one meeting point

Step-by-step solution

x2+y2−10x−10y+41=0{x}^{2} + {y}^{2} - 10x - 10y + 41 = 0

A(5,5),R1=3A ( 5, 5 ) , {R}_{1} = 3

x2+y2−22x−10y+137=0{x}^{2} + {y}^{2} - 22x - 10y + 137 = 0

B(11,5),R2=3B ( 11, 5 ) , {R}_{2} = 3

AB=6=R1+R2AB = 6 = {R}_{1} + {R}_{2}

Touch each other externally

⇒⇒ circles have only one meeting point.

Practice Circle on Quantrex Academy →

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