9'5 Hyperbolas

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9.5 Hyperbolas
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Essential Question

• How do I write the standard equation of
  hyperbolas, and how do I graph them?

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The standard equation of a hyperbola centered at
(h, k) is
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The standard equation of a hyperbola centered at
(h, k) is
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Write the standard equation for the hyperbola
with vertices at (0, -4) and (0, 4) and
co-vertices at (-3, 0) and (3, 0). Then sketch
the graph.
Because the vertices lie along the y-axis and the
center is at the origin, The equation is of the
form
From the coordinates of the vertices, a 4. From
the coordinates of the co-vertices, b 3.
Plot the vertices and co-vertices, and draw the
rectangle determined by these points. Sketch the
lines containing the diagonals of this rectangle.
Then sketch the branches of the hyperbola between
the lines that contain the diagonals.
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Write the standard equation of the hyperbola
with foci at (-1, 1) and (5, 1) and vertices at
(0, 1) and (4, 1).
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