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Notes For Ellipses

  • (intro) Planets travel in ________________ orbits.

    (page 1) The equation ____________________ represents a cirlce with radius |r|.

  • (page 1) The equation Ax2 + By2 = P represents an ellipse that is not a circle when A and B are _______________.

  • (page 2) The equation x2/ 16 + y2/ 9 = 1 represents an ellipse with x-intercepts at ( _____, 0) and ( _____, 0) and y-intercepts at (0, _____ ) and (0, _____ ).

  • (page 3) In an ellipse, the axis of symmetry parallel to the x-axis is called the ____________________ axis.
    The axis of symmetry parallel to the y-axis is called the ____________________ axis.

  • (page 3) The standard equation of an ellipse centred at the origin is ____________________.

  • (page 3) An ellipse centred at the origin with a horizontal axis of length 10 and a vertical axis of length 6 has the following standard equation: ____________________.

  • (page 3a) If |a| > |b|, the _______________ axis of the ellipse is longer than the _______________ axis.

  • (page 4) The standard equation of an ellipse centred at (h, k) is __________________________.

  • (page 4) Increasing the value of h moves the ellipse _______________.

  • (page 4) Decreasing the value of k moves the ellipse _______________.

  • (page 5) The general ellipse equation can be obtained by ____________ the standard equation.

  • (page 6) To rewrite the general equation into standard form, you use the method called _____________________________________________.

  • (page 9) An ellipse that is not a circle is formed when the double-napped cone is sliced with a plane that
    _______________________________________________________.