Page 79 - Calculus for the Clueless, Calc II

Just a few months after the first edition of this book went to press, I realized a second way to find the vertices
that made it much clearer to you, 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. Soooo, letting y =-4, we get

Therefore, x = 6 ± 11 and the major vertices are (6 ± 11 ,-4). Points north-south of (6,-4) have the same x
1/2
1/2
value, x = 6.

1/2
1/2
Therefore, y = -4 ± 8 , and the minor vertices are (6,-4 ± 8 ). For the same reasons the foci, always on the
major axis, are (6 ± 3 ,-4). The sketch is, of course, the same.
1/2
Example 9—

Sketch and discuss 4x + 5y + 30y - 40x + 45 = 0. Here we must complete the square in a slightly different
2
2
manner.

Center (5,-3); vertices ; ; foci . Of course, you
should put 5 instead of . I leave the for the sake of clarity.