ࡱ> MOLk{ =>=>_9 r&nE=>_9E=>=>VD@3E|QYk:D oEE0FE04Jy<4J3E4Jn3E<_9_9=>_9_9_9_9_9EE->_9_9_9F_9_9_9_94J_9_9_9_9_9_9_9_9_9 8: MATH 30 WC ELLIPSE 1. For each of the following, determine the center of the ellipse and the endpoints of each axis. a.  EMBED Equation.DSMT36  b.  EMBED Equation.DSMT36  c.  EMBED Equation.DSMT36  d.  EMBED Equation.DSMT36  e.  EMBED Equation.DSMT36  f.  EMBED Equation.DSMT36  Tough Question! 2. Sketch the graph of each of the ellipses in question 1 and check your graph on a graphing calculator. (Write the equation you need to put in your calculator) 3. Write the equation of each of the ellipses below.  a. b.  c. 4. Write the equation of an ellipse with a center (3, (2), passing through ((4, (2), (10, (2), (3, 1), and (3, 5). 5. For each ellipse, determine the coordinates of the center, the endpoints of the both axes. a.  EMBED Equation.DSMT36  b.  EMBED Equation.DSMT36  c.  EMBED Equation.DSMT36  d.  EMBED Equation.DSMT36  e.  EMBED Equation.DSMT36  f.  EMBED Equation.DSMT36  6. Change the following to general form. a.  EMBED Equation.DSMT36  b.  EMBED Equation.DSMT36  7. Find the equation of an ellipse satisfying the given conditions: a. center at (2, 5) with the longer axis of length 12 and parallel to the xaxis, shorter axis of length 10 b. center at ((3, 4) with the longer axis of length 8 and parallel to the yaxis, shorter axis of length 2 8. B.C. Place Stadium has an airfilled fabric dome roof that forms the shape of an ellipse when viewed from above. Its maximum length is approximately 230 m, its maximum width is approximately 190 m, and its maximum height is approximately 60 m. a. Find an equation for the ellipse formed by the base of the roof.  b. Taking a cross section of the roof at its greatest width results in a semiellipse. Find an equation for this semiellipse.  c. The promoters of a concert plan to send fireworks up from a point on the stage that is 30 m lower than the center in part b, and 40 m along the major axis of this ellipse from its center. How far is that point on the stage from the roof? 9. Describe the transformations (translations and stretches) that have been applied to the unit circle  EMBED Equation.DSMT36  to produce each of the ellipses below. Then find the standard form of the equation of each ellipse.  Ellipse Worksheet Answers For each of the following, determine the centre of the ellipse and the endpoints of each axis.  EMBED Equation.DSMT36  C(0,0), Endpts(8,0),(8,0),(0,6),(0,6)  EMBED Equation.DSMT36  C(0,0), Endpts(4,0),(4,0),(0,7),(0,7)  EMBED Equation.DSMT36  C(7,5), Endpts(9,5),(5,5),(7,0),(7,10)  EMBED Equation.DSMT36  C(3,8), Endpts(0,8),(6,8),(3,2),(3,18)  EMBED Equation.DSMT36  C(0,0), Endpts(4,0),(4,0),(0,3),(0,3)  EMBED Equation.DSMT36  C(2,1), Endpts EMBED Equation.DSMT4  Sketch the graph of each of the ellipses in question 1 and check your graph on a graphing calculator. (Write the equation you need to put in your calculator) Write the equation of each of the ellipses below.  EMBED Equation.DSMT4    EMBED Equation.DSMT4    EMBED Equation.DSMT4  Write the equation of an ellipse with a centre (3,2), passing through (4,2), (10,2), (3,1), and (3,5).  EMBED Equation.DSMT4  For each ellipse, determine the coordinates of the centre, the endpoints of the both axes.  EMBED Equation.DSMT36  C(1,4), Endpts EMBED Equation.DSMT4   EMBED Equation.DSMT36  C(0,3), Endpts(11,3),(11,3),(0,2),(0,4)  EMBED Equation.DSMT36  C(0.5,1), Endpts(4.5,1),(5.5,1),(0.5,2),(0.5,4)  EMBED Equation.DSMT36  C(3,1), Endpts(1,1),(5,1),(3,3),(3,5)  EMBED Equation.DSMT36  C(2,1), Endpts(1,1),(5,1),(2,3),(2,1)  EMBED Equation.DSMT36  C(1.5,1), Endpts(5.5,1),(2.5,1), (1.5,2),(1.5,4) Change the following to general form.  EMBED Equation.DSMT36   EMBED Equation.DSMT4   EMBED Equation.DSMT36   EMBED Equation.DSMT4  Find the equation of an ellipse satisfying the given conditions: Centre at (2,5) with the longer axis of length 12 and parallel to the xaxis, shorter axis of length 10.  EMBED Equation.DSMT4  Centre at (3,4) with the longer axis of length 8 and parallel to the yaxis, shorter axis of length 2  EMBED Equation.DSMT4  B.C. Place Stadium has an airfilled fabric dome roof that forms the shape of an ellipse when viewed from above. Its maximum length is approximately 230 m, its maximum width is approximately 190 m, and its maximum height is approximately 60 m. Find an equation for the ellipse formed by the base of the roof.    EMBED Equation.DSMT4  Taking a cross section of the roof at its greatest width results in a semiellipse. Find an equation for this semiellipse.   EMBED Equation.DSMT4  The promoters of a concert plan to send fireworks up from a point on the stage that is 30 m lower than the centre in part b), and 40 m along the major axis of this ellipse from its centre. How far is that point on the stage from the roof? 84.4 m Describe the transformations (translations and stretches) that have been applied to the unit circle  EMBED Equation.DSMT36  to produce each of the ellipses below. Then find the standard form of the equation of each ellipse. a) Vertical stretch by a factor of 3 about the xaxis, horizontal stretch by a factor of 2 about the yaxis, up 6, and left 3.  EMBED Equation.DSMT4  Vertical stretch by a factor of 3 about the xaxis, horizontal stretch by a factor of 2 about the yaxis, up 6, and left 3.  EMBED Equation.DSMT4  Vertical stretch by a factor of 3 about the xaxis, horizontal stretch by a factor of 2 about the yaxis, up 6, and left 3.  EMBED Equation.DSMT4  Vertical stretch by a factor of 3 about the xaxis, horizontal stretch by a factor of 2 about the yaxis, up 6, and left 3.  EMBED Equation.DSMT4  e) Vertical stretch by a factor of 3 about the xaxis, horizontal stretch by a factor of 2 about the yaxis, up 6, and left 3.  EMBED Equation.DSMT4      Page  PAGE 1 190 m 230 m 60 m 190 m a) e) d) f) c) b) 190 m 230 m 60 m 190 m a) e) d) f) c) b) CD     & ' ( ) . / G H I J O P h i j k Y [ t u ɿukj h(YCEHUj\u: h(YCUVjh(YCEHUjMu: h(YCUVjh(YCEHUj,u: h(YCUVjh h(YCEHUju: h(YCUVjh(YCEHUju: h(YCUVjh(YCEHUju: h(YCUVjh(YCUh(YC h(YC>* h(YC5*CD * K } ~ ! 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