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Stuck here, help me understand: - Co-ordinate geometry - JEE Main

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     

  • 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

 
Answers (1)
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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

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