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Most Important Selected Qs for JEE AdvancedMathematicsCircle

For the circles x^2+y^2-10 x+16 y+89-r^2=0 and x^2+y^2+6 x-14 y+42=0 which of the following is/are true.

Options

  1. ANumber of integral values of r are 7 for which circles are intersecting.
  2. BNumber of integral values of r are 9 for which circles are intersecting.
  3. CFor r equal to 13 number of common tangents are 3.
  4. DFor r equal to 21 number of common tangents are 2.

Correct answer

C. For r equal to 13 number of common tangents are 3.

Step-by-step solution

We have (x-5)^2+(y+8)^2=25+64+r^2-89 and (x+3)^2+(y-7)^2=49+9-42=16 aligned & (x-5)^2+(y+8)^2=r^2 & and (x+3)^2+(y-7)^2=(4)^2 aligned = 289 =17= distance between their centres aligned & Now, |r-4| 17 r+4 & r+4 17 & r 13 aligned aligned & and -17 r-4 17 & -13 r 21 & Hence, 13 r 21 aligned Possible values of 'r' can be 14,15,16,17,18,19,20 Hence required sum = 119

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