Question 1181121: Dear Sir,
Please help me solve this problem and please show your solution also because am really very slow in Math am already 61 years old.
Find the equation of the ellipse with center at (0, 0), length of major axis is 8, and a focus at (0, −2). Identify the parts of the ellipse and sketch the graph.
Parts of an Ellipse Graph of an Ellipse
1. Center
2. Foci
𝐹1
𝐹2
3. Vertices
𝑉1
𝑉2
4. Co-vertices
𝐵1
𝐵2
5. Endpoints of Latus
Rectum
𝐸1
𝐸2
𝐸3
𝐸4
6. Directrices
7. Eccentricity
8. Length of LR
9. Length of Major Axis
10.Length of Minor Axis
Thank you very much and God Bless you.
Lorna
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! Find the equation of the ellipse
with center at ( , ), => ,
the equation of the ellipse is
length of major axis is  =>
and a focus at (,  )
since a focus is at (,  )=>
and
other focus is on oposite side of the center at (,  )
your equation is: major axis is on y-axis, so  goes with 
1. Center (, )
2. Foci
𝐹1 (, )
𝐹2(, )
3. Vertices V =>(,),(, )
𝑉1 (, )
𝑉2(, )
4. Co-vertices =>( ,),( ,)
𝐵1( , )
𝐵2( , )
5. Endpoints of Latus
Rectum
𝐸1 ( ,  )=> ( ,  )=> ( , )
𝐸2( , )=> ( , )=> ( , )
𝐸3(,  )=> (,  )=> (, )
𝐸4(, )=> (, )=> (, )
6. Directrices:  , 
7. Eccentricity:
8. Length of LR:
First latus rectum: 
Second latus rectum:
The length of the latera recta:
9. Length of Major Axis:
10.Length of Minor Axis:
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