Part of CG-05 — Hyperbola

Asymptotes

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The asymptotes of x2x^2/a2a^2 - y2y^2/b2b^2 = 1 are y = +/-ba\frac{b}{a}x, obtained by setting the RHS to 0. The asymptotes pass through the centre and are diagonals of the rectangle with sides 2a and 2b. The angle between asymptotes is 2arctanba\frac{b}{a}. Key relations: equation of hyperbola + equation of conjugate = 2(equation of asymptotes). For a rectangular hyperbola (a = b), asymptotes are perpendicular (y = +/-x).

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