Multiple choice

The range of values of $\lambda$ for which the circles $ x^2 + y^2 = 4$ and $ x^2 + y^2 - 4\lambda x + 9 = 0$ have two common tangents is

  1. $ [-13/8 , 13/8]$
  2. $ > 13/8\ Or\ < -13/8$
  3. $(1, 13/8)$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For two circles to have two common tangents, they must intersect at two distinct points. This occurs when the distance between their centers is less than the sum of their radii and greater than the absolute difference of their radii.

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