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COMEDK2022MathematicsCircle

The circle x^2+y^2+4 x-7 y+12=0 cuts an intercept on Y -axis of length

Options

  1. A3
  2. B4
  3. C7
  4. D1

Correct answer

D. 1

Step-by-step solution

The equation of the circle is x^2 + y^2 + 4x - 7y + 12 = 0 . To find the intercept on the Y-axis, set x = 0 in the equation of the circle. 0^2 + y^2 + 4(0) - 7y + 12 = 0 y^2 - 7y + 12 = 0 Factoring the quadratic equation, we get (y - 3)(y - 4) = 0 . The roots are y₁ = 3 and y₂ = 4 . The length of the intercept on the Y-axis is |y₂ - y₁| = |4 - 3| = 1 . Answer: 1

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