Math151OldSols5

# Math151OldSols5 - QUIZ ON CHAPTER 12 SOLUTIONS MATH 151...

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QUIZ ON CHAPTER 12 SOLUTIONS MATH 151 – SPRING 2003 – KUNIYUKI 100 POINTS TOTAL You may use mixed numbers instead of improper fractions in your answers. Don’t approximate. 1) Consider the equation xy y +-+ = 64 8 9 3 0 2 . Its graph is a parabola in the standard xy -plane. (Show your work at the bottom of the page.) (13 points total) a) Which way does the parabola open (down, left, right, or up)? y y fy +- + = =- + - () 8 9 3 0 8 9 3 2 2 12 44 3 The equation expresses x as a function of y , so the parabola either opens right or left. The leading coefficient of is negative a < 60 , so the parabola opens left . b) What are the coordinates of the vertex of the parabola? ky b a = - = - coordinate of vertex 2 48 26 4 hx f = = =- () + () - = - coordinate of vertex 4 48 49 3 3 2 Vertex: 3, 4

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c) What are the coordinates of the focus of the parabola? Find p , the signed distance from the vertex to the focus. p a = = - () =- 1 4 1 46 1 24 The parabola opens left, so the focus lies to the left of the vertex. (Also, p < 0.) The vertex is at 34 , , so the focus lies at: 3 1 24 4 - Ê Ë Á ˆ ¯ ˜ Ê Ë Á ˆ ¯ ˜ , 2 23 24 ,4 2) Consider the equation 321 8 4 1 7 0 22 xy x y ++- + = . Its graph is an ellipse in the standard xy -plane. (Show your work at the bottom of the page.) (24 points total) 8 4 1 7 0 31 8 24 1 7 36 1 7 9 1 1 7 3 9 2 1 33 21 2 2 x y xx y y yy + = + +- + ++ + + () + + Group terms.
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## Math151OldSols5 - QUIZ ON CHAPTER 12 SOLUTIONS MATH 151...

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