Multiple choice

The length of the tangent from $(-3,1)$ to the circle $3x^2+3y^2-5x-6y-12=0$ is

  1. $3$
  2. $\sqrt{3}$
  3. $4$
  4. $\sqrt{5}$
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A Correct answer
Explanation

The length of the tangent from a point to a circle is given by the square root of the power of the point with respect to the circle. First, rewrite the circle equation as x^2 + y^2 - (5/3)x - 2y - 4 = 0. Substituting (-3, 1) into this expression gives sqrt((-3)^2 + 1^2 - (5/3)(-3) - 2(1) - 4) = sqrt(9 + 1 + 5 - 2 - 4) = sqrt(9) = 3.

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