Multiple choice

The length of the chord of the circle $x^{2}+y^{2}+4x-7y+12=0$ along the $y-$axis is

  1. $1$
  2. $2$
  3. $\dfrac{1}{2}$
  4. $None\ of\ these$
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A Correct answer
Explanation

The chord along the y-axis is found by setting x=0 in the circle equation: y^2 - 7y + 12 = 0. Factoring gives (y-3)(y-4) = 0. The points are (0,3) and (0,4). The length is |4-3| = 1.

AI explanation

To find the intercept on the y-axis, substitute x = 0 into the circle's equation to get y^2 - 7y + 12 = 0. Factoring this quadratic equation yields (y - 3)(y - 4) = 0, meaning the intersection points are (0, 3) and (0, 4). The length of the chord is the distance between these points, which is 4 - 3 = 1. The result is 1.

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