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Jonask

  • 2 years ago

prove that the directrix of an ellipse is \[x=\frac{a^2}{c}\]

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  1. Jonask
    • 2 years ago
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    this ellipse is the general ellipse with \[\frac{ x^2 }{ a^2}+\frac{ y^2 }{ b^2 }=1,a>b\]

  2. Jonask
    • 2 years ago
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    i have the proof but i dont understand the ratio set up here can i post the link

  3. Jonask
    • 2 years ago
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    http://mathworld.wolfram.com/Ellipse.html

  4. Jonask
    • 2 years ago
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    \[r=\frac{ a-c }{ d-a }=\frac{ a }{ d }\]

  5. Jonask
    • 2 years ago
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    \[a^2=b^2+c^2 i dont get this ratio .why it holds

  6. experimentX
    • 2 years ago
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    ??|dw:1364055606757:dw||dw:1364055629069:dw|

  7. experimentX
    • 2 years ago
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    i haven't done conics for quite while, but this shouldn't be difficult.|dw:1364055735803:dw|

  8. Jonask
    • 2 years ago
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    i mean http://mathworld.wolfram.com/images/equations/Ellipse/NumberedEquation12.gif

  9. experimentX
    • 2 years ago
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    what's r there?

  10. Jonask
    • 2 years ago
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    its defined in the 1st link

  11. experimentX
    • 2 years ago
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    can't find it ... equation no?

  12. Jonask
    • 2 years ago
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    24

  13. experimentX
    • 2 years ago
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    what is this 'c' again?

  14. experimentX
    • 2 years ago
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    this 'c' looks like foci.

  15. experimentX
    • 2 years ago
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    this is pretty ovbioius ... this ratio must be constant

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