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August 26th, 2017, 08:47 PM   #1
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Question The equation of all parabolas given a vertex and a point

"Find the equation of all parabolas having vertex (-2, -3), passing through (2, 1), and whose directrix is horizontal or vertical."

How do you find the one equation that would satisfy the given information?

My method of solving left me with 2 equations (one for each of the vertical and horizontal directrix).
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August 26th, 2017, 11:42 PM   #2
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I can't see how you would have the same equation for both orientations of the parabola.

One would be quadratic in $x$ the other would be quadratic in $y$
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August 27th, 2017, 04:17 AM   #3
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A vertical parabola is a function of x but not y. A horizontal parabola is a function of y but not x. There cannot be a formula in x and y only that gives both.
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