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I have a doubt, kindly clarify. - Two-dimensional Coordinate Geometry - BITSAT

The circles x^{2}+y^{2}+2x-2y+1=0\:and\:x^{2}+y^{2}-2x-2y+1=0\:touch\:each\:other

  • Option 1)

    extrernally at (0,1)

  • Option 2)

    Internally at (0,1)

  • Option 3)

    Externally at (1,0)

  • Option 4)

    Internally at (1,0)

 
Answers (1)
111 Views
V Vakul

 

Common tangents of two circles -

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

 

- wherein

 

 GC_{2}=\sqrt{(-1-1)^{2}+(-1+1)^{2}}=2

r_{1}=\sqrt{1+1-1}=1

r_{2}=\sqrt{1+1-1}=1

r_{1}+r_{2}=C_{1}C_{2}


Option 1)

extrernally at (0,1)

This is correct option

Option 2)

Internally at (0,1)

This is incorrect option

Option 3)

Externally at (1,0)

This is incorrect option

Option 4)

Internally at (1,0)

This is incorrect option

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