Rupert graphs the hyperbola (x+5)264−(y+2)236=1 . How does he proceed?

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Rupert first identifies the center of the hyperbola as , and that the hyperbola opens . Since a = , the coordinates of the vertices are Response area.

The slopes of the asymptotes of this parabola are ± Response area, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are Response area.

Once this information is gathered, the asymptotes are graphed as dashed lines, and the hyperbola is drawn through the vertices, approaching the asymptotes.