Conics q (1 Viewer)

[fine ambiguity]

I feel stoopid after staring at this for an hour. So productively I'll put it on here It's from the fitzpatrick textbook.

Using cartesian coordinates, show that the sum of the distances from any point P on the ellipse x^2 / a^2 + y^2 / b^2 = 1 to the foci is equal to 2a.

I have no idea where to begin. After my hour contemplation the only things I have concluded are 1 - I suck, and 2 - it does equal 2a, but I don't know how to show it.

 

[jonnathann]

I think this is the simplest method, but there are like a few so here goes.. P(x1,y1)
PS/PM = e
PS=ePM PS'=ePM'
=e(OM-NP) =e(NM+NP)
=e(a/e-x1) =e(a/e+x1)
=a-ex1 =a+ex1
PS+PS'=2a

 

[jonnathann]

oh yeh the diagram...

 

[fine ambiguity]

Hey, thanks very much!

 

[jonnathann]

no probzz.