Stitz-Zeager_College_Algebra_e-book

We have no idea how many variables may be involved so

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Unformatted text preview: they will be positioned at the foci of the ellipse? Solution. Graphing the data yields y 40 units tall x 100 units wide It’s most convenient to imagine this ellipse centered at (0, 0). Since the ellipse is 100 units wide and 40 units tall, we get a = 50 and b = 40. Hence, our ellipse has the equation x2 y2 + 2 = 1. 502 40 √ √ We’re looking for the foci, and we get c = 502 − 402 = 900 = 30, so that the foci are 30 units from the center. That means they are 50 − 30 = 20 units from the vertices. Hence, Jason and Jamie should stand 20 feet from opposite ends of the gallery. 428 7.4.1 Hooked on Conics Exercises 1. Graph the ellipse. Find the center, the lines which contain the major and minor axes, the vertices, the foci and the eccentricity. x2 y2 + =1 169 25 (x − 2)2 (y + 3)2 + =1 (b) 4 9 (x + 5)2 (y − 4)2 (c) + =1 16 1 2 2 (x − 1) (y − 3) (d) + =1 10 11 (e) (x − 1)2 (y + 3)2 + =1 9 4 (f) (x + 2)2 (y − 5)2 + =1 16 20 (g) (a) (x − 4)2 (y − 2)2 + =1 8 18 2. Put the equation in standard form. Find the center, the lines which contain the major and minor...
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