ckallerid
  • ckallerid
I require assisstance! Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1. f(x) = −one fourth x2 f(x) = one fourth x2 f(x) = −4x2 f(x) = 4x2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
What is the directrix? How can we use this to help us derive the parabola?
ckallerid
  • ckallerid
Honestly I have no clue, Can you give me like a quick run down on how to do any of this?
anonymous
  • anonymous
The directrix is a special line to the parabola. Consider some point on the parabola, then the distance from the diretrix to this point and the distance from the focus to this point are the same. Mathematically, we can write this as \[ (x-h)^2 + (y-k)^2 = (y-h_1)^2\], where (h,k) is the focus of the parabola and y = h_1 is the equation of the directrix. In this case, h = 0, k = 1, and h_1 = -1.

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anonymous
  • anonymous
Solve for y in this equation and you will get the equation of your parabola.
anonymous
  • anonymous
you can answer this in like two seconds if you know two things first, what does this look like?
ckallerid
  • ckallerid
a simple plug in problem.
anonymous
  • anonymous
|dw:1443317214435:dw|
anonymous
  • anonymous
there is a crude picture with a focus and directrix labelled do you know what the parabola looks like?
ckallerid
  • ckallerid
I'm guessing it would look vertical??
anonymous
  • anonymous
copy my picture and draw it
ckallerid
  • ckallerid
|dw:1443317495455:dw|(like I said I have no clue)
anonymous
  • anonymous
yeah i can see that
anonymous
  • anonymous
the vertex is half way between \((0,1)\) and \(y=-1\) like this
anonymous
  • anonymous
|dw:1443317677014:dw|
anonymous
  • anonymous
the point half way between \((0,1)\) and \(y=-1\) is \((0,0)\) so the vertex is at the origin, and the parabola opens up
anonymous
  • anonymous
that means it looks like \[4py=x^2\] where \(p\) is the distance between the vertex and the focus, or the vertex and the directrix in this case \(p=1\)
anonymous
  • anonymous
your answer is therefore \[4y=x^2\]
ckallerid
  • ckallerid
Didn't I need to solve for Y or something like that?
ckallerid
  • ckallerid
whatevs thanks guys!

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