Multiple choice

The length of the tangent from $(0,0)$ to the circle $2(x^{2}+y^{2})+x-y+5=0$, is

  1. $\sqrt {5}$
  2. $\sqrt {5}/2$
  3. $\sqrt {2}$
  4. $\sqrt {5/2}$
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D Correct answer
AI explanation

Divide the circle's equation by 2 to get the standard form x^2 + y^2 + x/2 - y/2 + 5/2 = 0. Applying the tangent length formula L = sqrt(x1^2 + y1^2 + 2gx1 + 2fy1 + c) for the point (0,0), we get L = sqrt(0 + 0 + 0 - 0 + 5/2). This simplifies directly to sqrt(5/2).

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