sleepyjess
  • sleepyjess
When using the equation y^2 = 4ax to find the equation of a parabola, how do I know what "a" is?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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sleepyjess
  • sleepyjess
Example, Question: Find an equation of the parabola with vertex at (0, 0) and focus at (3, 0). Solution: The distance form the vertex (0, 0) to the focus (3, 0) is a = 3. Based on equation 2, the equation of this parabola is \(y^2 = 4ax\) \(y^2 = 12x\)
sleepyjess
  • sleepyjess
Where do they get the 3 from?
TheSmartOne
  • TheSmartOne
They get the 3 from the focus. http://prntscr.com/9ds9no

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TheSmartOne
  • TheSmartOne
|dw:1450038495017:dw|
sleepyjess
  • sleepyjess
This was a huge struggle point last year for me >_<
sleepyjess
  • sleepyjess
So the x coordinate of the focus is "a"?
TheSmartOne
  • TheSmartOne
Yup :)
sleepyjess
  • sleepyjess
So, Question: Find an equation of the parabola with vertex at (1, 2) and focus at (4, 8). Would "a" still be 4?
TheSmartOne
  • TheSmartOne
And depending on the equation, the graph will look differently. And from the equation you can tell where the focus would be by knowing what 'a' is :)
sleepyjess
  • sleepyjess
Idek if that would be a possible vertex and focus, just an example
TheSmartOne
  • TheSmartOne
For that kind of question, you have to use another formula: (x-h)^2 = 4p(y-k)
sleepyjess
  • sleepyjess
How do I know what h, k and p are?
sleepyjess
  • sleepyjess
Vertex is (h, k) right?
TheSmartOne
  • TheSmartOne
As always, (h,k) is the vertex
TheSmartOne
  • TheSmartOne
And, for p "The absolute value of p is the distance between the vertex and the focus and the distance between the vertex and the directrix."
sleepyjess
  • sleepyjess
My book says 4a, is there any difference between p and a?
TheSmartOne
  • TheSmartOne
I guess not lol
TheSmartOne
  • TheSmartOne
http://www.purplemath.com/modules/parabola3.htm :)

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