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Example 1

Consider the equation

Given our comments above, this equation yields a parabola. (Note that this equation only has one square term. This indicates that we have a parabola here, as opposed to an ellipse or hyperbola.)

The value of d in this case is fairly clear; namely,

The vertex of this parabola is at and the axis of this parabola is vertical (since the variable x is the squared variable.) Thus, the focus of this parabola is situated at the point and the directrix is the horizontal line 2 units below the vertex. Thus, the equation of the directrix is given by

See Figure P7 for a sketch of this parabola.


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James A. Sellers