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Concept: General Second Degree Equation

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ax2 + 2hxy + by2 + 2gx + 2 fy + c = 0

  • Case 1: pair of straight line if abc+2fgh-af2-bg2-ch2=0
  • Case 2: abc+2fgh-af2-bg2-ch2≠0 then represents a parabola if h2= ab, ellipse if h2 < ab, and hyperbola if h2 > ab.
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