Question

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

Answer: (A)

Let Clie on $x^2+y^2=25$
Let $S$ be the set of circles with radius $3$ and center $(h,k)$
Any point $P(h,k)$ on $S$ will be $3$ units from center $C$.
Distance from origin will be at least $5-3=2$ and at most $5+3=8$
$\Rightarrow 2\le \sqrt{h^2+k^2}\le 8$
$4\le h^2+k^2\le 64$
Locus is
$4\le x^2+y^2\le 64$