Question

The centres of a set of circles, each radius $2$ lie on the circle $x^2+y^2=16$. The locus of any point lying inside the set of circle is

• A. $x^2+y^2\le 36$
• B. $4\le x^2+y^2$
• C. $4\le x^2+y^2\le 36$
• D. $1\le x^2+y^2\le 16$

Answer 1

The correct option is C $4\le x^2+y^2\le 36$

Let the locus be $(h,k)$ , the centre of the circle.
$r_1-r_2\le C_1{C}_2\le r_1+r_2$
$\Rightarrow 4-2\le \sqrt{h^2+k^2}\le 4+2$
$\Rightarrow 2\le \sqrt{h^2+k^2}\le 6$
$\Rightarrow 4\le h^2+k^2\le 36$
$\Rightarrow 4\le x^2+y^2\le 36$