List I
List II
A) An equation of the
circle touching the
x- axis is

1) $x^{2} + y^{2} + 2 a x + 2 a y + a^{2} = 0$
B) An equation of the
circle touching the
y- axis is
2) $x^{2} + y^{2} - 2 a x + 2 b y + b^{2} = 0 y$
C) An equation of the
circle touching both
the axes is
3) $x^{2} + y^{2} + 2 a x - 2 a y + a^{2} = 0$
D) An equation of the
circle passing through
(a, b) is
4) $x^{2} + y^{2} + a x - b y - 2 a^{2} = 0$

2, 3, 1, 4

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2, 1, 4, 3

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3, 2, 1, 4

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1, 2, 3, 4

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Solution

The correct option is D $1, 2, 3, 4$
for $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
A) equation of circle touching the x-axis have $g^{2} = a c$
$∴ a^{2} = 1 \times a^{2}$ True
$x^{2} + y^{2} + 2 a x + 2 a y + a^{2} = 0$
B) equation of circle touching y-axis has $f^{2} = a c$
$∴ x^{2} + y^{2} + 2 a x + 2 b y + b^{2} = 0$
has $b^{2} = 1 \times b^{2}$
C) equation of the circle touching both axes has
$f^{2} = a c a n d g^{2} = a c$
$∴ x^{2} + y^{2} + 2 a x - 2 a y + a^{2} = 0$
D) equation of circle passing through $(a, b)$ means
$e q^{n}$ of circles satisfies $(a, b)$ point
$∴ x^{2} + y^{2} + a x - b y - 2 a^{2} = 0$

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List I	List II
A) An equation of the circle touching the x- axis is	1) $x^{2} + y^{2} + 2 a x + 2 a y + a^{2} = 0$
B) An equation of the circle touching the y- axis is	2) $x^{2} + y^{2} - 2 a x + 2 b y + b^{2} = 0 y$
C) An equation of the circle touching both the axes is	3) $x^{2} + y^{2} + 2 a x - 2 a y + a^{2} = 0$
D) An equation of the circle passing through (a, b) is	4) $x^{2} + y^{2} + a x - b y - 2 a^{2} = 0$