Question

The centres of a set of circle, each of radius 3, lie on the circle $x^2+y^2=25$. The locus of any point inside the set of circle is

• A. $4\le x^2+y^2\le 64$
• B. $x^2+y^2\le 25$
• C. $x^2+y^2\ge 25$
• D. $3\le x^2+y^2\le 9$

Answer 1

The correct option is A $4\le x^2+y^2\le 64$

Let $(h,k)$ be any point in the set, then the equation of circle is
$(x-h{)}^2+(y-k{)}^2=9$
But $(h,k)$ lies on $x^2+y^2=25$,
$\Rightarrow h^2+k^2=25$
$\therefore 2\le$ Distance between the centres of two circles $\le$ 8
$4\le h^2+k^2\le 64$
$\therefore$, Locus of $(h,k)$ is $4\le x^2+y^2\le 64$
Hence, option 'A' is correct.