Page 105 - Calc for the Clueless

Example 18 Revisited—

Just a few months after the book went to press, I realized a second way to find the vertices that made it much
clearer, but my editor wouldn't change the book. So now I finally have a chance to show you.

The center is again at the point (6,-4). The vertices are directly east-west and north-south of the point (6,-4). All
points east-west of (6,-4) must have the same y value, y = -4. Sooo, letting y = -4, we get

Therefore x = 6 ± 11 and the major vertices are (6 ± 11 ,-4).
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Points north-south of (6,-4) have the same x value, x=6.

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1/2
Therefore Y = -4 ± 8 and the minor vertices are (6,-4 ± 8 ). For the same reasons the foci, always on the
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major axis, are (6 ± 3 ,-4). The sketch is, of course, the same.
Example 19—

2
Sketch and discuss 4x = 5y + 30y - 40x + 45 = 0.
2