## anonymous 3 years ago prove that the directrix of an ellipse is $x=\frac{a^2}{c}$

1. anonymous

this ellipse is the general ellipse with $\frac{ x^2 }{ a^2}+\frac{ y^2 }{ b^2 }=1,a>b$

2. anonymous

i have the proof but i dont understand the ratio set up here can i post the link

3. anonymous
4. anonymous

$r=\frac{ a-c }{ d-a }=\frac{ a }{ d }$

5. anonymous

\[a^2=b^2+c^2 i dont get this ratio .why it holds

6. experimentX

??|dw:1364055606757:dw||dw:1364055629069:dw|

7. experimentX

i haven't done conics for quite while, but this shouldn't be difficult.|dw:1364055735803:dw|

8. anonymous
9. experimentX

what's r there?

10. anonymous

its defined in the 1st link

11. experimentX

can't find it ... equation no?

12. anonymous

24

13. experimentX

what is this 'c' again?

14. experimentX

this 'c' looks like foci.

15. experimentX

this is pretty ovbioius ... this ratio must be constant