A circle is drawn touching the $x - a x i s$ and centre at the point which is the reflection of $(a, b)$ in the line $y - x = 0$ . The equation of the circle is-

x^{2} + y^{2} - 2 b x - 2 a y + a^{2} = 0

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x^{2} + y^{2} - 2 b x - 2 a y + b^{2} = 0

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x^{2} + y^{2} - 2 a x - 2 b y + b^{2} = 0

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x^{2} + y^{2} - 2 a x - 2 b y + a^{2} = 0

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Solution

The correct option is B $x^{2} + y^{2} - 2 b x - 2 a y + b^{2} = 0$
From figure,
Radius of the circle $= a$
and centre $\equiv (b, a)$
And circle is touching the x-axis.
The equation of the circle :
$x^{2} + y^{2} - 2 b x - 2 a y + b^{2} = 0$
Hence, B is the correct option.

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x^{2} + y^{2} + 2 a x + 2 b y + 1 = 0

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x^{2} + y^{2} + 2 a x + 2 b y + c = 0

x^{2} + y^{2} + 2 b x + 2 a y + c = 0

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) $x^{2} + y^{2} + a x - b y - 2 a^{2} = 0$

The two circles $x^{2} + y^{2} + 2 a x + c = 0 a n d x^{2} + y^{2} + 2 b y + c = 0$ touch if $\frac{1}{a^{2}} + \frac{1}{b^{2}} =$

x^{2} + y^{2} + 2 a x + c^{2} = 0

x^{2} + y^{2} + 2 b y + c^{2} = 0

\frac{1}{a^{2}} + \frac{1}{b^{2}} = \frac{1}{c^{2}}

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