Stitz-Zeager_College_Algebra_e-book

Check your answer algebraically and graphically 1 2 2x

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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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