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The equation of an ex-circle of a triangle formed by the common tangents to the circle x 2 + y 2 = 4 and x 2 + y 2 - 6 x + 8 = 0 is

Options

  1. Ax 2 + y 2 = 4
  2. Bx 2 + y 2 - 6 x + 8 = 0
  3. Cx 2 + y 2 - 6 x + 9 = 0
  4. Dx 2 + y 2 = 1

Correct answer

A. x 2 + y 2 = 4

Step-by-step solution

For x 2 + y 2 = 2 2 , the centre is 0 , 0 and radius is 2 units and for x 2 + y 2 - 6 x + 8 = 0 , the centre is 3 , 0 and radius is 1 unit Now, note that the circles touch each other externally, hence the larger circle is an excircle of the triangle formed by the common tangents.

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