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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 + 26 = 0 , is

Options

  1. A4
  2. B1
  3. C2
  4. D3

Correct answer

D. 3

Step-by-step solution

Given x 2 + y 2 - 4 x - 6 y - 1 2 = 0 C 1 2 ,   3 ,   r 1 = 2 2 + 3 2 + 12 = 25 = 5 And x 2 + y 2 + 6 x + 1 8 y + 2 6 = 0 C 2 - 3 , - 9 ,   r 2 = 3 2 + 9 2 - 26 = 9 0 - 2 6 = 8 Then, C 1 C 2 = 5 2 + 1 2 2 = 1 3 C 1 C 2 = r 1 + r 2 ⇒ Externally touching circles. ⇒ 3 common tangents.

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