Multiple choice

The lengths of the tangents from $(1,0), (2,0), (3,2)$ to a circle are $1, \sqrt{7},\sqrt{2}$. Then the equation of the circle is

  1. $\mathrm{x}^{2}+\mathrm{y}^{2}+6\mathrm{x}+17\mathrm{y}+6=0$
  2. $2\mathrm{x}^{2}+2\mathrm{y}^{2}+6\mathrm{x}-17\mathrm{y}-6=0$
  3. $2\mathrm{x}^{2}+2\mathrm{y}^{2}-6\mathrm{x}-17\mathrm{y}-6=0$
  4. $2\mathrm{x}^{2}+2\mathrm{y}^{2}-6\mathrm{x}-17\mathrm{y}+6=0$
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B Correct answer
Explanation

The length of the tangent from (x1, y1) to circle x^2 + y^2 + 2gx + 2fy + c = 0 is sqrt(x1^2 + y1^2 + 2gx1 + 2fy1 + c). Using the given points, we set up a system of equations to solve for g, f, and c.

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