Multiple choice

Find the length of intercept made by the circle $x^{2}+y^{2}+2x+3$ -5=0 on:

  1. x axis

  2. y axis

  3. on the line x = y chord cut by the circle intercept

  4. None of these
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A Correct answer
AI explanation

The equation of the circle is found by simplifying the given expression to x^2+y^2+2x-2=0, placing its center at (-1, 0) with a radius squared of 3. To find the x-axis intercept, set y = 0, which results in the quadratic equation x^2+2x-2=0. Solving this equation yields roots where the difference between them (the intercept length) is 2 times the square root of (1 squared minus (-2)), equaling 2 times the square root of 3.

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