# The centres of a set of circles, each of radius 3, lie on the circle $\dpi{100} x^{2}+y^{2}=25.$ The locus of any point in the set is      Option 1) $4\leq x^{2}+y^{2}\leq 64\;$ Option 2) $\; x^{2}+y^{2}\leq 25\;$ Option 3) $\; \; x^{2}+y^{2}\geq 25\;$ Option 4) $\; 3\leq x^{2}+y^{2}\leq 9$

As we learnt in

Common tangents of two circle -

Where two circle neither intersect nor touch each other, there are 4 common tangents.Two are transverse and two are direct common tangents.

- wherein

and

Common tangents of two circle -

When they intersect, there are two common tangents, both of them being direct.

- wherein

and

Common tangents of two circles -

When two circles touch  each other externally, there are three common tangents, two of them are direct.

- wherein

We should have

$OA\leqslant OP\leqslant OB$

So, $(5-3)\leqslant \sqrt{x^{2}+y^{2}}\leqslant 5+3$

$4\leqslant x^{2}+y^{2}\leqslant 64$

Option 1)

$4\leq x^{2}+y^{2}\leq 64\;$

This option is correct

Option 2)

$\; x^{2}+y^{2}\leq 25\;$

This option is incorrect

Option 3)

$\; \; x^{2}+y^{2}\geq 25\;$

This option is incorrect

Option 4)

$\; 3\leq x^{2}+y^{2}\leq 9$

This option is incorrect

Exams
Articles
Questions