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MHT CET202617 April 2026Morning ShiftMathematicsCircleActual

If a circle passes through the points (2,3) and (4,5) and its center lies on the straight line y - 4x + 3 = 0 , then its equation is......

Options

  1. Ax^2 + y^2 - 4x - 10y + 25 = 0
  2. Bx^2 + y^2 - 4x - 10y - 25 = 0
  3. Cx^2 + y^2 - 4x + 10y - 25 = 0
  4. Dx^2 + y^2 + 25 = 0

Correct answer

A. x^2 + y^2 - 4x - 10y + 25 = 0

Step-by-step solution

Let the equation of the circle be x^2 + y^2 + 2gx + 2fy + c = 0 . The center of the circle is (-g, -f) . Since the center lies on the line y - 4x + 3 = 0 : -f - 4(-g) + 3 = 0 4g - f + 3 = 0 The circle passes through (2, 3) , so substituting x = 2, y = 3 : 2^2 + 3^2 + 2g(2) + 2f(3) + c = 0 4g + 6f + c + 13 = 0 The circle passes through (4, 5) , so substituting x = 4, y = 5 : 4^2 + 5^2 + 2g(4) + 2f(5) + c = 0 8g + 10f + c + 41 = 0 Subtracting the equation for (2, 3) from the equation for (4, 5) : (8g - 4g) + (10f - 6

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