My Math Forum Parabola and Directrix and Focus, Oh MY!!!

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 November 15th, 2010, 01:28 PM #1 Senior Member   Joined: Apr 2009 Posts: 106 Thanks: 0 Parabola and Directrix and Focus, Oh MY!!! For the parabola y = x^2 I have determined that the focus is the point (0, 1/4) I have determined that the directrix is the line y = -1/4 Am I correct?
 November 15th, 2010, 01:48 PM #2 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: Parabola and Directrix and Focus, Oh MY!!! Yes, that is correct. For the parabola whose axis of symmetry is the y-axis and whose vertex is at the origin,i.e $y=kx^2$ the focus will be at $\left(0,\frac{1}{4k}\right)$ and the directrix will be the line $y=-\frac{1}{4k}$, which can be found using the definition of the parabola, i.e., the locus of all points being equidistant from a fixed line, the directrix, and a fixed point not on the line, the focus.
February 21st, 2013, 09:00 PM   #3
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Re: Parabola and Directrix and Focus, Oh MY!!!

Quote:
 Originally Posted by julian21 For the parabola y = x^2 I have determined that the focus is the point (0, 1/4) I have determined that the directrix is the line y = -1/4 Am I correct?
Whether something is correct depends on HOW you determine it. Did you read it in a book? Saw it on Youtube? Your classmate pass you a note during a quiz? You determine if something is correct by DOING it. CONSTRUCT the parabola, like this.

http://www.flickr.com/photos/85937466@N ... hotostream

or this

 Tags directrix, focus, parabola

### find the equation of the ellipse with foci and directrix

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