Vertices, foci, asymptotes and graph from center and semi-axes.
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Why it works
A hyperbola is the set of points whose distances to two foci differ by 2a. Here c² = a² + b² (note the plus — unlike the ellipse), so the foci sit farther out; the asymptotes y−k = ±(b/a)(x−h) are the diagonals of the central box the branches approach.