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For the hyperbola given by 2x² + 5xy + 2y² + 4x + 5y = 0, the equation representing the pair of its asymptotes is
- 2x² + 5xy + 2y² + 4x + 5y + 2 = 0
- 2x² + 5xy + 2y² + 4x - 5y + 2 = 0
- 2x² + 5xy + 2y² = 0
- None of these
Correct answer: 2x² + 5xy + 2y² + 4x + 5y + 2 = 0
Solution
Asymptotes have the same second-degree part plus a constant: 2x^2+5xy+2y^2+4x+5y+c = 0 must represent two lines, so its 3x3 determinant vanishes. Solving gives c = 2, so the asymptote pair is 2x^2+5xy+2y^2+4x+5y+2 = 0.
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