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If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre is
  • a)
    2ax - 2by - (a2 +b2 + 4)=0 [2004]
  • b)
    2ax + 2by - (a2 + b2 + 4)=0
  • c)
    2ax - 2by + (a2 + b2 + 4)=0
  • d)
    2ax + 2by + (a2 + b2 + 4)=0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If a circle passes through the point (a, b) and cuts the circle x2 + y...
Let the variable circle is x2 + y2 + 2gx + 2fy + c = 0 ......(1)
It passes through (a, b)
∴ a2 + b2 + 2 ga + 2 fb + c = 0 ......(2)
(1) cuts x2 +y2= 4 orthogonally
∴2(gx0+ f x0) = c-4 ⇒ c=4
∴ from (2) a2 + b2 + 2ga + 2fb + 4=0
∴  Locus of centre (–g,–f) is a2 + b2 - 2ax -2by +4= 0
or 2ax + 2by = a2 + b+ 4
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If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre isa)2ax - 2by - (a2 +b2 + 4)=0 [2004]b)2ax + 2by - (a2 + b2 + 4)=0c)2ax - 2by + (a2 + b2 + 4)=0d)2ax + 2by + (a2 + b2 + 4)=0Correct answer is option 'B'. Can you explain this answer?
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If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre isa)2ax - 2by - (a2 +b2 + 4)=0 [2004]b)2ax + 2by - (a2 + b2 + 4)=0c)2ax - 2by + (a2 + b2 + 4)=0d)2ax + 2by + (a2 + b2 + 4)=0Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre isa)2ax - 2by - (a2 +b2 + 4)=0 [2004]b)2ax + 2by - (a2 + b2 + 4)=0c)2ax - 2by + (a2 + b2 + 4)=0d)2ax + 2by + (a2 + b2 + 4)=0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre isa)2ax - 2by - (a2 +b2 + 4)=0 [2004]b)2ax + 2by - (a2 + b2 + 4)=0c)2ax - 2by + (a2 + b2 + 4)=0d)2ax + 2by + (a2 + b2 + 4)=0Correct answer is option 'B'. Can you explain this answer?.
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