Multiple choice

What is the length of common tangents of the circles $x^{2}+y^{2}=6x, x^{2}+y^{2}+2x=0$

  1. $\sqrt{3}$
  2. $\sqrt{3},3\sqrt{3}$
  3. $2\sqrt{3}$
  4. $2\sqrt{3},3\sqrt{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Circle 1: center (3,0), r1=3. Circle 2: center (-1,0), r2=1. Distance between centers d=4. Since d > r1+r2 (4 > 4 is false, d=r1+r2), they touch externally. Length of common tangent is sqrt(d^2 - (r1-r2)^2) = sqrt(16 - 4) = sqrt(12) = 2*sqrt(3).

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