Math Is Fun Forum

octonion

Member

Registered: 2007-06-11

Posts: 6

ellipse

the sum of the distances from the point (x,y) on an ellipse to the points (-e,0) and (e,0) (where e>0) is constant and equal to S. Use this characterization of the ellipse to show that its equation in the xy-plane is x^2/a^2  + y^2/b^2 = 1, where a^2 = (S/2)^2 and b^2 = (S/2)^2 - e^2

I am using the vector form for the 2 distances, and I get S^2 = 4(x^2) + 4(y^2)
where did I go wrong?

Thanks to all for your help!

Last edited by octonion (2007-06-11 02:22:00)

---

And(we will) take upon's the mystery of things,
As if we were God's spies.
King Lear

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: ellipse

The total distance of red line segments together is S.

---

X'(y-Xβ)=0

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: ellipse

[Edited wrong working.]

Last edited by JaneFairfax (2007-06-12 09:46:43)

octonion

Member

Registered: 2007-06-11

Posts: 6

Re: ellipse

JaneFairfax, thanks for your  help. I have a question though: how can you get only positive terms inside the square root, even after simplification, when you have negative terms? I did expand and simplify several times, and I get a     

term!!
This is driving me mad!

Last edited by octonion (2007-06-12 11:03:40)

---

And(we will) take upon's the mystery of things,
As if we were God's spies.
King Lear

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: ellipse

I’m sorry, I made a mistake. The expression inside the square root should actually be

Sorry, my working above is wrong.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: ellipse

Right, this is my working (hopefully correct this time).

Last edited by JaneFairfax (2007-06-12 10:35:51)

octonion

Member

Registered: 2007-06-11

Posts: 6

Re: ellipse

Now I agree! and as we say in my country, merci...

---

And(we will) take upon's the mystery of things,
As if we were God's spies.
King Lear

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: ellipse

Il n’y a pas de quoi. J’aime aider tout le monde.

By the way, the eccentricity of this ellipse is e⁄a.