Question

Find the product of the real values 'a' such that the equation \[ax^{2} + 2y^{2} - 4y + 2(1 - a) = 0\]represents an ellipse with latus rectum of length 1.

Answer 1

Write the equation in standard form

Answer 2

\[ax^2+2(y^2-2y+1)-2a=0\]

Answer 3

\[\frac{x^2}{2}+\frac{(y-1)^2}{a}=1\]

Answer 4

Alright, I get how we got to standard form, but how do we find out the values of a? I got this far yesterday, but I don't know what to do from here.

Answer 5

do u know what is the latus rectum formula for standard form of ellipse

Answer 6

Isn't it b^2/a? I think that's what someone said when I asked it yesterday.

Answer 7

2b^2/a

Answer 8

values of a and b for this equation?

Answer 9

Well, I don't know because isn't a the bigger one? Would it be:
4/√a = 1
a = 16
OR
2a/√2 = 1
2a = √2
a = √2/2
Then the product:
16√2/2 = 8√2
Is that right?

Answer 10

if a>b latus rectum=2b^2/a
if a<b latus rectum=2a^2/b

Answer 11

\[a=\sqrt{2} \ \ and \ \ b=\sqrt{a}\]

Answer 12

Ok, I figured all that stuff out before I solved for a, so did I get it right 8√2?

Answer 13

thats right

Answer 14

Alright. Thank you!

Answer 15

HELP PLEASE!!!! find the equation of ellipse. center @origin.
1. Passing through (-2, 9/4), vertex at (4,0)
2.

Answer 16

If the length of latus rectum is 4 and distance between the foci is 4radical2, then find the standard equation of ellipse.

Answer 17

Ellipse, center at (0, -1), length of latus rectum is 16/3, distance between foci is 4sqrt5.

Answer 18

Find the equation of an ellipse whose center at (1, 5), major axis parallel to OX

Answer 19

Find e of an ellipse if the distance between its foci is same as the length of it

Answer 20

I will give medal :
Find the equation of the ellipse given the eccentricity 2/3, latus rectum 2/3.

Answer 21

I will give medal :
Find the equation of the ellipse given latus rectum 60/19, d

Answer 22

I will give medal :
Find the equation of the ellipse given the latus rectum 4, d

Answer 23

I will give medal :
Find the equation of the ellipse passing through (2,3),latus rectum three times the distance from the center to focus.

Answer 24

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Answer 25

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Answer 26

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Answer 27

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Answer 28

Can someone please help me with an overdue assignment?

Answer 29

6^4=1,296 in log form?

Answer 30

What sentence accurately completes the proof

Answer 31

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Answer 32

What is a pair of elements that would be expected to form an ionic bond?

Answer 33

What is a pair of elements that would be expected to form an ionic bond?

Answer 34

Dose wood working count as art? Oh well

Answer 35

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