maths
posted by muzungu
Given that the ellipse x^2/a^2 + y^2/b^2 =1 has foci at(+/ae,0)where e is the eccentricity and b^2=a^2(1e^2),find the coordinates of the foci and the value of e^2 for the ellipse X^2+4y^2 =16

L.Bianchessi
Well you subtract the 16 to get your equation equal to one.
Do x^2/16 + y^2/4=1
Your center is 0,0
Your eclipse would be horizontal.
Do when graphing put a point at (0,0) then go 4 spaces in the negative and positive direction on the xaxis. Then go up 2 spaces from (0,0) in the positive and negative directions on the yaxis. Put your points on the graph. Draw your ellipse.
Then you know to find your c, you do c^2=a^2 b^2. So that's c^2= 164. Which makes c=2radical3
Eccentricity= c/a
So 2radical3/ 4.......e= radical 3 / 2
Foci= (+/ 2radical3, 0)
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