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TS EAMCET · Maths · Circle

A line is at a constant distance \(c\) from the origin and meets the coordinate axes in \(A\) and \(B\). The locus of the centre of the circle passing through \(O, A, B\) is

  1. A \(x^2+y^2=c^2\)
  2. B \(x^2+y^2=2 c^2\)
  3. C \(x^2+y^2=3 c^2\)
  4. D \(x^2+y^2=4 c^2\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x^2+y^2=4 c^2\)

Step-by-step Solution

Detailed explanation

Let the equation of the circle be \[ x^2+y^2+2 g x+2 f y+c=0 \] It passes through origin \[ \text { so } c=0 \] Then, the equation of circle is \[ x^2+y^2+2 g x+2 f y=0 \] It also passes through \(A\left(x_1, 0\right)\)…