Multiple choice

The length of tangent from the point $(-1,2)$ to the circle $x^2 + y^2 - 8x + 5y - 7 = 0$.

  1. $1$
  2. $4$
  3. $2$
  4. $6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The length of the tangent from (x1, y1) to a circle x^2 + y^2 + 2gx + 2fy + c = 0 is sqrt(x1^2 + y1^2 + 2gx1 + 2fy1 + c). Here, x1=-1, y1=2, g=-4, f=2.5, c=-7. Length = sqrt((-1)^2 + 2^2 - 8(-1) + 5(2) - 7) = sqrt(1 + 4 + 8 + 10 - 7) = sqrt(16) = 4.

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