by Kristina Dunbar, UGA
Parabolas do not have to be centered at the origin or facing up. The directrix and focus can be anywhere. Below are some examples of parabolas with different foci and directrixes.
Example 1:
directrix: y = 1
focus: origin
With the directrix above the focus, the parabola now opens downward.
Example 2:
directrix: y = -4
focus: (1, 0)
The parabola is now wider than previous parabolas.
Example 3:
directrix: x = 1
focus: origin
This parabola looks like the standard parabola we started with in the first part of the exercise, but it opens to the left.
Example 4:
directrix: y = x
focus: (1, -1)
This parabola is opening up and to the left (the line y = -x bisects the parabola).
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