Multiple choice

Length of the tangent drawn from point $(1, 5)$ to the circle $2x^2+2y^2=3$ is?

  1. $7$
  2. $7\sqrt{2}$
  3. $7\sqrt{2}/2$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Circle equation: x^2 + y^2 = 3/2. Radius r = sqrt(1.5). Point (1, 5). Length of tangent = sqrt(x1^2 + y1^2 - r^2) = sqrt(1^2 + 5^2 - 1.5) = sqrt(1 + 25 - 1.5) = sqrt(24.5) = sqrt(49/2) = 7/sqrt(2) = 7*sqrt(2)/2.

AI explanation

First, divide the circle's equation 2x^2 + 2y^2 = 3 by 2 to get x^2 + y^2 = 1.5. The formula for the length of the tangent from an external point (x1, y1) is the square root of S1. Substituting (1, 5) into x^2 + y^2 - 1.5 gives 1^2 + 5^2 - 1.5 = 1 + 25 - 1.5 = 24.5. The square root of 24.5 is 7 times the square root of 2, all divided by 2.

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