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

x^{2} + y^{2} = 20

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x^{2} + y^{2} - 2 x - 4 y = 0

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x^{2} + y^{2} = 4

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x^{2} + y^{2} = 16

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Solution

The correct option is A $x^{2} + y^{2} - 2 x - 4 y = 0$
Given points are $(2, 0)$ and $(0, 4)$

Therefore, equation of circle is $(x - 2) (x - 0) + (y - 0) (y - 4) = 0$

By expanding, we get

$x^{2} - 2 x + y^{2} - 4 y = 0$

Option B is correct.

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