Find the equation of the director circle of a circle
$x^{2} + y^{2} = 100$

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Solution

The given circle is
$x^{2} + y^{2} = 100$ .... (i)
Comparing with $x^{2} + y^{2} = a^{2}$ , we get
$a^{2} = 100$ .... (ii)
The equation of the director circle of circle (i) is
$x^{2} + y^{2} = 2 a^{2}$
$\Rightarrow x^{2} + y^{2} = 2 (100)$ ....[From (ii)]
$\Rightarrow x^{2} + y^{2} = 200$ .

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