Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Which equations represent a hyperbola?

Algebra

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  • 2 months ago

      The equations which represent a hyperbola: 

      A   (x + 1)^2/3 + (y - 5)^2/7 = 1 

      B   (x + 1)^2/3 - (y - 5)^2/7 = 1                      ====> Answer

      C   25x^2 - y^2 + 150x - 14y + 174 = 0         ====> Answer

      D   x^2/4 + y^2/9 = 1

  • Pope
    Lv 7
    2 months ago

    None of the equations has an xy term. The discriminant is positive if the x² and y² terms are on the same side of the equation and have opposite signs. That includes equations B and C. Equation B is in standard form, which is possible only for a hyperbola. Equation C is in general form. Before calling it a hyperbola you must confirm that it is not a degenerate. It actually is a hyperbola. One way to prove that would be to complete the squares and write it in standard form.

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