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Observe the lists :
List - I
A) Equation of the circle touching the x-axis
B) Equation of the circle touching the y-axis
C) Equation of circle touching both the axis
D) Equation of the circle passing through (a, b)
List - II
1) $x^{2} + y^{2} + 2 a x + 2 a y + a^{2} = 0$
2) $x^{2} + y^{2} - 2 a x + 2 b y + b^{2} = 0$
3) $x^{2} + y^{2} + 2 a x - 2 b y + a^{2} = 0$
4) $x^{2} + y^{2} + a x - b y - 2 a^{2} = 0$
The correct match is :

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$A - 2, B - 1, C - 4, D - 3$

$A - 1, B - 2, C - 4, D - 3$

$A - 3, B - 2, C - 1, D - 4$

$A - 3, B - 2, C - 4, D - 1$

answer is C.

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Detailed Solution

Touch x-axes $= g^{2} = c$

Touch y-axes $\Rightarrow f^{2} = c$

Touch both axes $g^{2} = f^{2} = c$ and verify options.

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