SOLUTION: Hey. My name is Anne. Nice to meet your lovely self. ^_^ Conics confuse me completely. Right now my class is on ellipses. So my question is how do I find an equation of an ellipse

Question 835350: Hey. My name is Anne. Nice to meet your lovely self. ^_^
Conics confuse me completely. Right now my class is on ellipses. So my question is how do I find an equation of an ellipse? It gave me a graph, and a couple points. The major axis is vertical, and the vertex is (0,10) and (0,-10). The focus is at (0,8) and (0,-8).
I know there's some kind of equation to put these numbers in, but somehow that did not end up in my notes! :(
While I'm asking, how would I do this when the major axis is horizontal? (I know that's asking 2 questions. I understand if you can't, or won't answer that one. I just need the equation.)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
How do I find an equation of an ellipse? It gave me a graph, and a couple points. The major axis is vertical, and the vertex is (0,10) and (0,-10). The focus is at (0,8) and (0,-8).
***
When trying to find the equation for a given ellipse, you must first determine whether it has a vertical or horizontal major axis.
..
If major axis is vertical,
Standard form of equation for the ellipse:
, a>b,(h,k)=(x,y) coordinates of center
..
If major axis is horizontal,
Standard form of equation for the ellipse:
, a>b,(h,k)=(x,y) coordinates of center
(notice the only change is a^2 and b^2 swapping places)
..
Now, for your given ellipse problem:
Gleaned from the 2 given points of the vertex,
x-coordinate of center=0
y-coordinate of center=0
so,center(0,0)
a=10(given distance from center to vertices on the vertical major axis)
a^2=100
..
c=8(given distance from center to foci on the vertical major axis)
c^2=64
..
c^2=a^2-b^2
b^2=a^2-c^2=100-64=36
b=√36=6
..
equation:

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