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MHT CET202613 April 2026Evening ShiftMathematicsCircleActual

The equation of the circle concentric with circle x^2 + y^2 - 6x + 7 = 0 and which touches the line x + y + 3 = 0 is ....

Options

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

Correct answer

B. x^2 + y^2 - 6x - 9 = 0

Step-by-step solution

The given circle is x^2 + y^2 - 6x + 7 = 0 . Its center is (3, 0) . The required circle is concentric with the given circle, so its center is also (3, 0) . The required circle touches the line x + y + 3 = 0 . The radius r of the required circle is the perpendicular distance from the center (3, 0) to the line x + y + 3 = 0 . r = |3 + 0 + 3| 1^2 + 1^2 = 6 2 = 3 2 The equation of the required circle is (x - 3)^2 + (y - 0)^2 = r^2 . (x - 3)^2 + y^2 = (3 2 )^2 x^2 - 6x + 9 + y^2 = 18 x^2 + y^2 - 6x - 9 = 0 Answer: x^2 +

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