Vertical Ellipse (CONICS) (1 Viewer)

[DraconisV]

The equation of the ellipse is x^2/4 + y^2/25 = 1.

The questions I have are:

1) is this ellipse vertical, as in the foci are on the y-axis?
2) is the major axis on the y-axis?
3) are the directrices vertical or horizontal?

I have for working out:

a^2=4, b^2=25

b^2=a^2(1-e^2)

25 =4(1-e^2)

25/4 = 1 - e^2

21/4 = e^2 (e^2 is (+)ve because e is a lenght)

e = (sq rt) of 21 over 4

Foci= (0, +/- (sq rt) 21)

Directrices= +/- 10/(sq rt) 21

now if the directrices are horizontal then they are y= +/- 10/(sq rt 21) which is
+/- ~2.18. if the directrices are y= +/- ~2.18 then they will pass through the ellipse.??? Something must be wrong here.

Any help will be greatly appreciated. Thank you.

 

[Rax]

Man I have e= (sqrt) of 21 over 5, working out rest still. That may affect

 

[Rax]

Ok here is my working rush job and I aint the most crazy person at Ext II so others may correct me.....(unfortunately)

x^2/4 + y^2/25=1

This means that a=5 (semi-major axis)
and b=2

e^2=1 - b^2/a^2
= 25/25 - 4/25
= 21/25
Thus e= (sqrt) 21/5

Foci =ae
5x (sqrt)21/5
=(sqrt)21

Thus foci are (0, +/- (sqrt) 21)

Directrices are a/e
=5/ (sqrt)21/5
=5x5/(sqrt) 21
= 25/(sqrt) 21

Thus directrices are y= +/- 25/ (sqrt)21

Thar we go, I didnt double check so yeh hope it helps. Man that took heaps to type

edit: Just remember for ellipses as a= semi major axis and e<1, a is always the biggest denom even if it is under the y

 

[DraconisV]

Thank you alot Rex, it clears it all up now. That point about the biggest number under either x^2 or y^2 is a, that made it better. Thank you.

 

[Rax]

Its Rax, lol but thanks anyway
Keep up the maths...........wait till you do some parametric form of the ellipse locus questions..they can take awhile
cya