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JEE Main 2004
Exam
JEE Main
Year
2004
Subject
Mathematics
Chapter
Circle

JEE Main 2004 · Mathematics · Circle

If a circle passes through the point (a, b) and cuts the circle...

If a circle passes through the point (a,b)(a, b) and cuts the circle x2+y2=4x^2+y^2=4 orthogonally, then the locus of its centre is

Options

  1. A2ax+2by+(a2+b2+4)=02 a x+2 b y+\left(a^2+b^2+4\right)=0
  2. B2ax+2by−(a2+b2+4)=02 a x+2 b y-\left(a^2+b^2+4\right)=0
  3. C2ax−2by+(a2+b2+4)=02 a x-2 b y+\left(a^2+b^2+4\right)=0
  4. D2ax−2by−(a2+b2+4)=02 a x-2 b y-\left(a^2+b^2+4\right)=0

Correct answer

B. 2ax+2by−(a2+b2+4)=02 a x+2 b y-\left(a^2+b^2+4\right)=0

Step-by-step solution

Let the circle be x2+y2+2gx+2fy+c=0⇒c=4anditpassesthroughx^2+y^2+2 g x+2 f y+c=0 \Rightarrow c=4 and it passes through(a, b) \Rightarrow \mathrm{a}^2+\mathrm{b}^2+2 \mathrm{ga}+2 \mathrm{fb}+4=0HencelocusofthecentreisHence locus of the centre is2 a x+2 b y-\left(a^2+b^2+4\right)=0
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