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  • How to solve this problem- - If the circles and intersect at two distinct points, then: - Co-ordinate geometry - JEE Main

If the circles x^2+y^{2}-16x-20y+164 = r^{2}  

and (x-4)^{2}+(y-7)^{2}=36

intersect at two distinct points, then:

  • Option 1)

     

    1< r <11

  • Option 2)

     

    r = 11

  • Option 3)

     

    r>11

  • Option 4)

     

    0 < r < 1

Answers (1)

best_answer

 

Common tangents of two circle -

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

|r_1-r_2|<\left|C_1C_2\right|<r_1+r_2

- wherein

 

From the concept 

centre of the circle (-g,-f)

A = (8,10)

 and R1 = r

Similarly,

B = (4,7), R2 = 6

|R1 - R2| < AB < R1 + R2

1 < r < 11


Option 1)

 

1< r <11

Option 2)

 

r = 11

Option 3)

 

r>11

Option 4)

 

0 < r < 1

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