Exercises on Ellipses Centered at the Origin   1.  For the ellipse               x2            y2                          +                  =  1              9              4 the x-axis the ______________ axis and the y-axis is the ______________ axis. 2.  For the ellipse               x2            y2                          +                  =  1              4              9 the x-axis the ______________ axis and the y-axis is the ______________ axis. For exercises 3 and 4, answer true or false and explain your reasoning. 3.  Ellipses are never graphs of functions. 4.  The graph of 4x2 + 25y2 =  36 is not an ellipse since the right hand side is not equal to 1. For exercises 5 - 12, sketch the graph of the given ellipse. 5.          x2            y2                          +                  =  1             25             9 6.          x2            y2                          +                  =  1              4             36 7.          x2            y2                          +                  =  1             36            49 8.          x2            y2                          +                  =  1             36             25 9.                    y2                x2  +                 =  1                         4 10.          x2                                +   y2       =  1              9               11.          x2             y2                          +                  =  1             5               16 12.                       y2                 x2   +                  =  1                           7 For exercises 9 - 32, sketch of the graph of the given ellipse.   13.                      y2                9x2  +                 =  1                          4 14.         x2                                +   16y2       =  1              4               15.     25x2  +  y2  =  1 16.      x2   +   16y2   =  1 17.     4x2  +  9y2  =  1 18.     100x2   +   81y2   =  1 19.     3x2  +  10y2  =  1 20.     18x2   +   11y2   =  1 21.     x2  +  4y2  =  16 22.     9x2   +   y2   =  36 23.     x2  +  25y2  =  25 24.     25x2   +   4y2   = 100 25.     x2  +  4y2  =  9 26.     16x2   +   y2   =  25 27.     25 x2  +  36y2  =  9 28.     36x2   +   25y2   =  49 29.     9 x2  +  12y2  =  12 30.     4x2   +   64y2   =  8 31.     x2  +  10y2  =  5 32.     6x2   +   15y2   =  9 For exercises 33 - 38 find the equation of the ellipse. 33.          34.  35.  36.    37.  38.  39.  Two of the vertices of an ellipse centered at the origin are (3,0) and (0,-4).  What are the other two vertices? 40.  Two of the vertices of an ellipse centered at the origin are (-5,0) and (0,1).  What are the other two vertices? 41.  One of the vertices of an ellipse centered at the origin is (3,0).  If the ellipse passes through the point (1,8/3), find the equation of the ellipse. 42.  One of the vertices of an ellipse centered at the origin is (0,-10).  If the ellipse passes through the point (,5), find the equation of the ellipse. 43.  One of the vertices of an ellipse centered at the origin is (-3,0).  If the ellipse passes through the point (,2), find the equation of the ellipse. 44.  Go to the site, Cool Math, and give two examples of how ellipses appear in the "real world".   Back to The Conic Page Back to the Math 154 Page Back to the Math Department Home Page