Unformatted text preview: eft and right of the center. In this case, as√
we’ve seen in the
derivation, the distance from the center to the focus, c, can be found by c = a2 − b2 . If b > a,
the roles of the major and minor axes are reversed, and the foci lie above and below the center.
√
In this case, c = b2 − a2 . In either case, c is the distance from the center to each focus, and
√
c = bigger denominator − smaller denominator. Finally, it is worth mentioning that if we take
the standard equation of a circle, Equation 7.1, and divide both sides by r2 , we get
Equation 7.5. The Alternate Standard Equation of a Circle: The equation of a circle
with center (h, k ) and radius r > 0 is
(x − h)2 (y − k )2
+
=1
r2
r2
Notice the similarity between Equation 7.4 and Equation 7.5. Both equations involve a sum of
squares equal to 1; the diﬀerence is that with a circle, the denominators are the same, and with an
ellipse, they are diﬀerent. If we take a transformational approach, we can consider both equations
as shifts and stretches of the Unit Circle x2 + y 2 =...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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