Math151OldSols5

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online