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AP EAMCET · Maths · Circle

The equation of the circle passing through \((2,0)\) and \((0,4)\) and having the minimum radius, is

  1. A \(x^2 + y^2 = 20\)
  2. B \(x^2 + y^2 - 2x - 4y = 0\)
  3. C \(x^2 + y^2 = 4\)
  4. D \(x^2 + y^2 = 16\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x^2 + y^2 - 2x - 4y = 0\)

Step-by-step Solution

Detailed explanation

Center \( (h,k) = \left(\frac{2+0}{2}, \frac{0+4}{2}\right) = (1,2) \) Radius squared \( r^2 = (2-1)^2 + (0-2)^2 = 1^2 + (-2)^2 = 1+4 = 5 \) Equation of circle: \( (x-1)^2 + (y-2)^2 = 5 \) \( x^2 - 2x + 1 + y^2 - 4y + 4 = 5 \) \( x^2 + y^2 - 2x - 4y = 0 \)