Explanation

(c)
Since, the equation of tangents $x - y - 2 = 0\$and $x - y + 2 = 0\$are parallel.
$\therefore$ Distance between them=Diameter of the circle$= \frac{2 - ( - 2)}{\sqrt{1^{2} + 1^{2}}}$
$\left( \because\ \ \frac{c_{2} - c_{1}}{\sqrt{a^{2} + b^{2}}} \right)$
$= \frac{4}{\sqrt{2}} = 2\sqrt{2}$
[image:11_image77.emf]
$\therefore\ \ \ Radius = \frac{1}{2}\left( 2\sqrt{2} \right) = \sqrt{2}$
It is clear from the figure that centre lies on the origin.
$\therefore$Equation of circle is
$(x - 0)^{2} + (y - 0)^{2} = \left( \sqrt{2} \right)^{2}$
$\ \Rightarrow \ x^{2} + y^{2} = 2$