The number of common tangents to the circles x 2 + y 2 - 4 x - 6 y - 1 2 = 0 and x 2 + y 2 + 6 x + 1 8 y +…

The number of common tangents to the circles x 2 + y 2 - 4 x - 6 y - 1 2 = 0 and x2+y2+6x+18y+26=0, is
  1. 4
  2. 1
  3. 2
  4. 3

Solution

Given  x 2 + y 2 - 4 x - 6 y - 1 2 = 0

C12, 3, r1=22+32+12=25=5

And x2+y2+6x+18y+26=0

C2-3,-9, r2=32+92-26

=90-26=8

Then, C1C2=52+122=13

C1C2=r1+r2

⇒Externally touching circles.

⇒3 common tangents.

Asked in: JEE Main 2015 (04 Apr)

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