Multiple choice

The length of the tangent drawn from the point $ (4,-1) $ to the circle $2x^2 + 2y^2 = 1$ is :

  1. $ \sqrt { \dfrac{17}{2} } $
  2. $ \sqrt {33} $
  3. $ \sqrt { \dfrac{33}{2} } $
  4. $ \sqrt2 $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The length of the tangent from (x1, y1) to x^2 + y^2 = r^2 is sqrt(x1^2 + y1^2 - r^2). Here, the circle is x^2 + y^2 = 1/2. Length = sqrt(4^2 + (-1)^2 - 1/2) = sqrt(16 + 1 - 0.5) = sqrt(16.5) = sqrt(33/2).

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