Question

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

• A. $4x^2+y^2=64$
• B. $x^2+4y^2=64$
• C. $x^2+4y^2=16$
• D. $4x^2+y^2=16$

Answer 1

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

Centre and radius of the circle $x^2+y^2=25$ are $(0,0)$ and $5$ respectively.
Thus required locus is $(5-3{)}^2\le x^2+y^2\le (5+3{)}^2$
$\Rightarrow 4\le x^2+y^2\le 64$