Question

Finding equation of an Ellipse from 2 points?

Answer 1

Hey, so I'm given 2 points on an ellipse: (-1,1) and (.5/-2)

Answer 2

No idea what to do here.

Answer 3

Those points are the foci?

Answer 4

No, they're just points on the ellipse

Answer 5

Oh, and the ellipse is in standard position, so I'm assuming center is 0,0

Answer 6

But the two foci must be different, lest it be a circle...

Answer 7

Yeah.

Answer 8

I need to find the equation of the ellipse, not the foci

Answer 9

So I imagine finding the vertices would be easier and using x^2/a^2 + y^2/b^2 = 1 would be easier?

Answer 10

oh yeah i would use this formula

Answer 11

So how do I find a and b?

Answer 12

by plugging the two points in, i think?

Answer 13

Well that doesn't do me much good cause then I'm left with 2 variables?

Answer 14

but you have two equations?

Answer 15

Yeah, and if I set them equal I still have two variables, right?

Answer 16

Well you have two equations for two unknowns, so they're sufficient? :)

Answer 17

I dunno. I have: \[1/b^2 + 1/ c^2 =1 \] and \[.25/b^2 +4/c^2 =1\]

Answer 18

but I dunno what to do with them. If I set them equal I get \[.75/b^2 =3/c^2\] and that doesn't help me?

Answer 19

Don't set them equal :)

Answer 20

What do I do then?

Answer 21

Two ways to go: Substitution or Elimination :)

Answer 22

Ohhh

Answer 23

God I'm dumb, yeah, that would make sense

Answer 24

no you're not dumb :)
your brain is just temporarily stuck :)

Answer 25

Appreciate the help man

Answer 26

no problem :)