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August 26th, 2017, 08:47 PM  #1 
Newbie Joined: Aug 2017 From: USA Posts: 1 Thanks: 0  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). 
August 26th, 2017, 11:42 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,944 Thanks: 1011 
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 $y$ 
August 27th, 2017, 04:17 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,170 Thanks: 869 
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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equation, parabolas, point, vertex 
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