Multiple choice

The distance of the point $(1, 2)$ from the common chord of the circles ${x}^{2}+{y}^{2}+6{x}-16=0$ and ${x}^{2}+{y}^{2}-2{x}-6{y}-6=0$ is

  1. $1$
  2. $\dfrac15$
  3. $5$
  4. $2$
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A Correct answer
Explanation

Common chord equation: S1 - S2 = 0. (x^2+y^2+6x-16) - (x^2+y^2-2x-6y-6) = 8x+6y-10 = 0, or 4x+3y-5 = 0. Distance from (1,2) to 4x+3y-5=0 is |4(1)+3(2)-5| / sqrt(4^2+3^2) = |4+6-5| / 5 = 5/5 = 1.

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