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anonymous

  • one year ago

Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1.

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  1. anonymous
    • one year ago
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    @zepdrix

  2. zepdrix
    • one year ago
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    eyyy

  3. zepdrix
    • one year ago
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    I think I remember you asking this yesterday? :O

  4. zepdrix
    • one year ago
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    |dw:1438975490650:dw|

  5. zepdrix
    • one year ago
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    Our Vertex is always equidistant from our focus and directrix, ya? So that puts us at 0,0

  6. zepdrix
    • one year ago
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    |dw:1438975604620:dw|

  7. zepdrix
    • one year ago
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    Umm from here... we can either do it the long way... or use that nice shortcut formula.. im trying to remember what it looks like..

  8. zepdrix
    • one year ago
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    Here is that shortcut that I was thinking of: \[\large\rm (x - h)^2 = 4p (y - k)\]Where our vertex is the point (h,k), and p is the distance between the focus and vertex.

  9. anonymous
    • one year ago
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    yes thank you i did ask yesterday but i had trouble at the end and couldnt find a :(

  10. anonymous
    • one year ago
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    h and k i got as 0, 0

  11. zepdrix
    • one year ago
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    \[\large\rm (x-0)^2=4p(y-0)\]\[\large\rm x^2=4py\]Ok good. let's solve for y,\[\large\rm y=\frac{1}{4p}x^2\]

  12. zepdrix
    • one year ago
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    And then, what is the value of p? The distance from the vertex up to the focus?

  13. anonymous
    • one year ago
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    wouldnt it be 2? from 1 to -1? or no

  14. zepdrix
    • one year ago
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    |dw:1438975963650:dw|No that would be 2p :)

  15. anonymous
    • one year ago
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    |dw:1438976050358:dw|is this the focus? at 0,1

  16. zepdrix
    • one year ago
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    |dw:1438976120582:dw|yes :) i want to know the distance from here to here from the VERTEX to the FOCUS. not from the DIRECTRIX silly :)

  17. anonymous
    • one year ago
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    ohhh 1

  18. anonymous
    • one year ago
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    sorry sorry

  19. zepdrix
    • one year ago
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    \[\large\rm y=\frac{1}{4p}x^2 \qquad\to\qquad y=\frac{1}{4\cdot1}x^2\]

  20. zepdrix
    • one year ago
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    Yayyy team, we did it! \c:/

  21. anonymous
    • one year ago
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    okay i got it now thank you soo much

  22. anonymous
    • one year ago
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    :))

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