Multiple choice

The range of $\lambda$ for which the variable line $3x+4y=\lambda$ lies between the circle ${x}^{2}+{y}^{2}-2x-2y+1=0$ and ${x}^{2}+{y}^{2}-18x-2y+78=0$ without intercepting a chord on either circles

  1. $(12,41)$
  2. $(12,31)$
  3. $(12,21)$
  4. $(2,41)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The line 3x+4y=lambda must lie between the two circles. The centers are (1,1) and (9,1) with radii 1 and 5 respectively. The distance from the center to the line must be greater than the radius for no intersection. Calculating the range for lambda leads to (12, 21).

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