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anonymous

  • one year ago

Find the vertex, focus, directrix, and focal width of the parabola. x = 4y^2

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  1. perl
    • one year ago
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    The general form of your parabola is $$ \Large x = \frac {1}{4p} y^2 $$Focal width is 4p

  2. anonymous
    • one year ago
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    ok what do i do wuth that formula

  3. perl
    • one year ago
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    we need to solve 1/(4p) = 4

  4. anonymous
    • one year ago
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    oh so p = 1/16?

  5. perl
    • one year ago
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    yes

  6. perl
    • one year ago
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    the vertex is (h,k) directrix is x = -p focal width is 4p

  7. perl
    • one year ago
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    it is centered at the origin

  8. anonymous
    • one year ago
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    how do we find h and k

  9. anonymous
    • one year ago
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    ok the focal width is .25

  10. perl
    • one year ago
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    The general form of a parabola that opens to the right or left \[ \Large x-h = \frac {1}{4p} (y-k)^2 \]Vertex is (h,k) directrix is x =h -p focal width is 4p

  11. perl
    • one year ago
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    yes that is correct

  12. anonymous
    • one year ago
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    is the focal width represented as a single letter?

  13. perl
    • one year ago
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    4 times that value of p

  14. anonymous
    • one year ago
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    like i know i can plug in x as 4y^2 but thats still not enough to find either h or k

  15. perl
    • one year ago
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    h must be zero and k must be zero

  16. anonymous
    • one year ago
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    how do you know its at the origin though

  17. anonymous
    • one year ago
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    oh wait all the choices have the vertix set to (0,0) but if it isnt how do you know

  18. perl
    • one year ago
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    \[ \Large x-h = \frac {1}{4p} (y-k)^2 \iff x = \frac {1}{4p} y^2 \]

  19. perl
    • one year ago
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    the two equation left sides must match and the right side must match

  20. anonymous
    • one year ago
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    ohhhhhh omg ok i get it

  21. perl
    • one year ago
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    the two equations left sides must match and right sides

  22. anonymous
    • one year ago
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    and thats how you know its at the origin?

  23. perl
    • one year ago
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    yes. or by graphing it

  24. anonymous
    • one year ago
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    ok then the directrix is 0-.25 which would = -1/4

  25. anonymous
    • one year ago
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    but what about the focus?

  26. perl
    • one year ago
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    correct. and the focus is (h+ p, k )

  27. anonymous
    • one year ago
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    oh ok this is actually simplier than i thought! thank you so much!

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