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July 5th, 2012, 03:42 AM  #1  
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Finding equation of parabola with focus and directrix Quote:
Using the form , I plugged in the vertex already. To find the value of 'p' I needed to use the distance formula for between either the focus and vertex, or the vertex and directrix which I know should be exactly the same. So I did: So: Put in standard form: I don't know if I've made any careless errors and I didn't want to rationalize the denominator and risk messing this up, but when I try to graph this, the graph of the parabola passes through the directrix...I thought it wasn't supposed to touch it at all?  
July 5th, 2012, 08:15 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Finding equation of parabola with focus and directrix
The axis of symmetry of the parabola is perpendicular to the directrix. If the directrix is y = x + 2, your parabola should be oriented at a 45 degree angle.

July 5th, 2012, 08:25 AM  #3 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Finding equation of parabola with focus and directrix
When you write "Using the form...", you are using the form of a VERTICAL parabola. Your equation will: 1. Contain an "xy" term, and 2. Not be a function of x (I.e. not pass the vertical line test) 
July 5th, 2012, 09:44 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Finding equation of parabola with focus and directrix
One method we could use is to find the locus of all points equidistant from the focus and directrix: Here is a plot of the parabola, directrix, and the axis of symmetry for the parabola: [attachment=0:1qw49g56]slantparabola.jpg[/attachment:1qw49g56] 

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directrix, equation, finding, focus, parabola 
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