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The circle x^2+y^2+3 x-y+2=0 cuts an intercept on X -axis of length

Options

  1. A2
  2. B3
  3. C1
  4. D4

Correct answer

C. 1

Step-by-step solution

The equation of the circle is x^2 + y^2 + 3x - y + 2 = 0 . To find the intercept on the X -axis, set y = 0 in the equation of the circle: x^2 + 3x + 2 = 0 Factor the quadratic equation: (x + 1)(x + 2) = 0 The roots are x₁ = -1 and x₂ = -2 . These are the points where the circle intersects the X -axis, specifically (-1, 0) and (-2, 0) . The length of the intercept on the X -axis is the absolute difference between these x -coordinates: Length = |x₁ - x₂| = |-1 - (-2)| = |-1 + 2| = 1 . Answer: 1

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