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. $4 \leq x^2 + y^2 \leq 64$
• B. $ x^2 + y^2 \leq 25 $
• C. $x^2 + y^2 \geq 25 $
• D. $3 \leq x^2 + y^2 \leq 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 $5+3=8$
$\Rightarrow 2 \leq \sqrt{ h ^{2}+ k ^{2}} \leq 8$
$4 \leq h ^{2}+ k ^{2} \leq 64$
Locus is
$4 \leq x^{2}+y^{2} \leq 64$