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MHT CET202525 Apr 2025Evening ShiftMathematicsCircleActual

If a circle with centre at (-1,1) touches the line x+2 y+4=0 then the co-ordinates of the point of contact are

Options

  1. A(-2,-1)
  2. B(8,-6)
  3. C(-10,3)
  4. D(-4,0)

Correct answer

A. (-2,-1)

Step-by-step solution

The point of contact between the circle centered at C(-1, 1) and the tangent line x + 2y + 4 = 0 lies at the foot of the perpendicular from the center to the line. The slope of the tangent line is m_L = - 1 2 , so the perpendicular line through C has slope m_ CP = 2 . This gives the equation y - 1 = 2(x + 1) , or 2x - y + 3 = 0 . Solving the system between this perpendicular and the tangent line: substituting y = 2x + 3 into x + 2y + 4 = 0 yields x + 2(2x + 3) + 4 = 0 , simplifying to 5x + 10 = 0 , so x = -2 and y

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