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anonymous

  • one year ago

Derive the equation of the parabola with a focus at (−7, 5) and a directrix of y = −11. a) f(x) = −one eighth (x − 2)2 + 6 b)f(x) = one eighth (x − 2)2 + 6 c)f(x) = −one eighth (x + 2)2 + 8 d)f(x) = one eighth (x + 2)2 + 8

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  1. anonymous
    • one year ago
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    please help

  2. anonymous
    • one year ago
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    sec just making sure my numbers work

  3. anonymous
    • one year ago
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    thank you ive narrowed it down to either a or c but i dont know what to do for there

  4. amistre64
    • one year ago
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    one method is to define all points (x,y) that are equidistance from a focus (a,b) and a directrix (in this case y=k) - which is just the point (x,k) (x-a)^2 + (y-b)^2 = (x-x)^2 + (y-k)^2

  5. amistre64
    • one year ago
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    (x-a)^2 + y^2 -2by +b^2 = y^2 -2ky +k^2 (x-a)^2 -2by +b^2 = -2ky +k^2 (x-a)^2 +(b^2-k^2) = 2by -2ky (x-a)^2 +(b^2-k^2) = 2(b-k)y (x-a)^2/(2(b-k)) +(b^2-k^2)/(2(b-k)) = y (x-a)^2/(2(b-k)) +(b+k)/2 = y

  6. amistre64
    • one year ago
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    none of your options fit ...

  7. anonymous
    • one year ago
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    if you use the formula \[y=a(x-h)^2+k \] where P = -7 Q = 5 and R = -11 and where a = \[\frac{ 1 }{ 2Q-2R }\] H = P and \[K = \frac{ Q + R }{ 2 }\] you can just plug in the values and solve

  8. anonymous
    • one year ago
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    I got that problem too.

  9. amistre64
    • one year ago
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    we know the options are bad or something off, since the parabola opens up its vertex x is the same value as the focus x ... (x+7)^2 is the main part

  10. amistre64
    • one year ago
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    its y value is the average of the focus y and the directrix (5-11)/2 = -3

  11. amistre64
    • one year ago
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    y = a(x+7)^2 - 3

  12. anonymous
    • one year ago
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    a = 1/32

  13. amistre64
    • one year ago
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    yep

  14. amistre64
    • one year ago
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    can you screen shot it?

  15. anonymous
    • one year ago
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    ya that's why I didn't reply faster... I was wondering if my math was bad or something haha

  16. amistre64
    • one year ago
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    some people tend to post the answers for one with the question of another

  17. anonymous
    • one year ago
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    oh my i am so sorry i realized the problem

  18. anonymous
    • one year ago
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    two of the questions were switched because those look like they would work for Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8

  19. amistre64
    • one year ago
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    never be afraid of your own errors ... they might prove to be correct int he end :)

  20. anonymous
    • one year ago
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    Using either of the 2 methods posted above with the new data should give you the answer :)

  21. anonymous
    • one year ago
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    thank yall sorry

  22. anonymous
    • one year ago
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    Np.

  23. amistre64
    • one year ago
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    good luck :)

  24. anonymous
    • one year ago
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    so its a

  25. anonymous
    • one year ago
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    thank you all so much that was very helpful

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