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JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 80

The number of common tangents to the circles x2+y2−4x−6y−12=0x^2+y^2-4x-6y-12=0 and x2+y2+6x+18y+26=0x^2+y^2+6x+18y+26=0, is :

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Answer and worked solution

Official answer: C

  • First circle: centre (2, 3), radius 5.
  • Second circle: centre (−3, −9), radius 9+81−26=8\sqrt{9+81-26}=8.

The centres are 13 apart, which is r1+r2r_1+r_2: the circles touch externally, so there are 3 common tangents.

Topics:Tangents and normals
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