Multiple choice

The length of tangent from the point (2, -3) to the circle 2x2 + 2y2 = 1 is

  1. 5
    • 5

  3. 5 / √ 2

  4. 6
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C Correct answer
Explanation

The circle is x^2 + y^2 = 0.5. The length of the tangent from (x1, y1) to x^2 + y^2 - r^2 = 0 is sqrt(x1^2 + y1^2 - r^2). Here, sqrt(2^2 + (-3)^2 - 0.5) = sqrt(4 + 9 - 0.5) = sqrt(12.5) = sqrt(25/2) = 5/sqrt(2).

AI explanation

Dividing the circle's equation by 2 gives x^2 + y^2 = 1/2, showing a radius squared of 1/2 centered at the origin. The length of the tangent from an external point (x1, y1) is found using the formula L = sqrt(x1^2 + y1^2 - r^2). Plugging in the point (2, -3) gives L = sqrt(2^2 + (-3)^2 - 1/2) = sqrt(4 + 9 - 0.5) = sqrt(12.5) = 5 / sqrt(2).

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