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# Which equations represent a hyperbola?

Algebra

### 2 Answers

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- KrishnamurthyLv 72 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

- PopeLv 72 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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