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TS EAMCET · Maths · Circle

The locus of the centre of circles passing through \((a, b)\) and cut the circle \(x^2+y^2-2 x+4 y-4=0\) orthogonally is

  1. A \((a+1) x+(b+2) y=\frac{a^2+b^2+4}{2}\)
  2. B \((a+1) x+(b-2) y=\frac{a^2+b^2+4}{2}\)
  3. C \((a-1) x+(b+2) y=\left(\frac{a^2+b^2+4}{2}\right)\)
  4. D \((a-1) x+(b-2) y=\frac{a^2+b^2+4}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((a-1) x+(b+2) y=\left(\frac{a^2+b^2+4}{2}\right)\)

Step-by-step Solution

Detailed explanation

Let the equation of one of the circles be \[ x^2+y^2+2 g x+2 f y+c=0 \] Since, it passes through \((a, b)\). Hence, \(a^2+b^2+2 g a+2 f b+c=0\) Also, it cuts the circle \(x^2+y^2-2 x+4 y-4=0\) orthogonally.…