For  the  two  circles  x^{2}+y^{2}=16 and x^{2}+y^{2}-2y=0, there is/are :

  • Option 1)

      one pair of common tangents   
     

  • Option 2)

     two pairs of common tangents  
     

  • Option 3)

    three common tangents   
     

  • Option 4)

     no common tangent   

 

Answers (1)

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

 

Common tangents of two circle -

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

- wherein

 

 

Common tangents of two circles -

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

 

- wherein

 

Common tangents of two circles -

When two circles touch each other internally, there is only one common tangent.

- wherein

 

S_{1}:x^{2}+y^{2}=16

r_{1}=4,\:C_{1}:\left ( 0,0 \right )

S_{2}:x^{2}+y^{2}-2y=0

r_{2}=1,\:C_{1}:\left ( 0,1 \right )

C_{1}C_{2}=1\:and\:r_{1}-r_{2}=3

There will be no tangent.

 

  

 

 

 


Option 1)

  one pair of common tangents   
 

This option is incorrect.

Option 2)

 two pairs of common tangents  
 

This option is incorrect.

Option 3)

three common tangents   
 

This option is incorrect.

Option 4)

 no common tangent   

This option is correct.

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