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 with such circle is

• A. $4\le x^2+y^2\le 64$
• B. $x^2+y^2\le 5$
• C. $x^2+y^2\le 25$
• 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 C lie 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 $5+3=8$

$⟹2\le \sqrt{h^2+k^2}\le 8$

$4\le h^2+k^2\le 64$

Locus is

$4\le x^2+y^2\le 64$