quiz9ans - ocus: ( 10 , 0) Directrix: x = 2 rom this...

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Math 222, Quiz 9 Name: Instructions: Answer the following questions completely, showing work where necessary. 1) Name the conic section represnted by the given equation. By completing the square, Fnd the center, foci, vertices, asymptotes, and radius, as appropriate. 4 x 2 + y 2 - 8 x - 2 y = - 1 By completing the square, we get the equation ( x - 1) 2 + ( y - 1) 2 4 = 4. Thus, this is an ellipse, with center (1 , 1). c = 4 - 1 = 3, and y is the major axis, so the foci are (1 , 1 ± 3). ±inally, the vertices are (1 , 1 ± 2). 2) The following information is given for a hyperbola centered at the origin. ±ind the eccentricity, standard-form equation, and asymptotes.
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Unformatted text preview: ocus: ( 10 , 0) Directrix: x = 2 rom this information, we get c = 10 and a e = 2. Use this to get that a 2 = 20, e = 4 5, b 2 = 10- 20. Thus, the standard form equation is x 2 20-y 2 10- 20 = 1, and the asymptotes are y = r 10- 20 20 x . Bonus (1 pt): How many dierent people have been President of the United States? There have been 43 presidents, but Grover Cleveland served non-consecutive terms (i.e. he was the 22nd and 24th president). Thus, there have only been 42 dierent presidents. 1...
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