anonymous
  • anonymous
prove that the directrix of an ellipse is \[x=\frac{a^2}{c}\]
Geometry
chestercat
  • chestercat
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anonymous
  • anonymous
this ellipse is the general ellipse with \[\frac{ x^2 }{ a^2}+\frac{ y^2 }{ b^2 }=1,a>b\]
anonymous
  • anonymous
i have the proof but i dont understand the ratio set up here can i post the link
anonymous
  • anonymous
http://mathworld.wolfram.com/Ellipse.html

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anonymous
  • anonymous
\[r=\frac{ a-c }{ d-a }=\frac{ a }{ d }\]
anonymous
  • anonymous
\[a^2=b^2+c^2 i dont get this ratio .why it holds
experimentX
  • experimentX
??|dw:1364055606757:dw||dw:1364055629069:dw|
experimentX
  • experimentX
i haven't done conics for quite while, but this shouldn't be difficult.|dw:1364055735803:dw|
anonymous
  • anonymous
i mean http://mathworld.wolfram.com/images/equations/Ellipse/NumberedEquation12.gif
experimentX
  • experimentX
what's r there?
anonymous
  • anonymous
its defined in the 1st link
experimentX
  • experimentX
can't find it ... equation no?
anonymous
  • anonymous
24
experimentX
  • experimentX
what is this 'c' again?
experimentX
  • experimentX
this 'c' looks like foci.
experimentX
  • experimentX
this is pretty ovbioius ... this ratio must be constant

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