Multiple choice

The number of common tangents to two circles x2 + y2 = 4 and x2 + y2 - 8x + 12 = 0 is

  1. 1

  2. 2

  3. 3

  4. 4

  5. 5
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C Correct answer
Explanation

The first circle has center (0,0) and radius 2. The second circle has center (4,0) and radius 2. The distance between centers is 4, which equals the sum of the radii (2+2), meaning the circles touch externally; therefore, they have 3 common tangents.

AI explanation

The first circle is x squared plus y squared equals 4, giving it a center at (0, 0) and a radius of 2. The second equation is rewritten by completing the square as (x minus 4) squared plus y squared equals 4, showing its center is at (4, 0) with a radius of 2. The distance between the centers is 4, which equals the sum of the radii (2 plus 2), meaning the two circles touch each other externally. Two circles touching externally have exactly 3 common tangents.

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