Answer to Question #25466 in Analytic Geometry for scofeild ivan

Question

find the equation of the ellipse with eccentricity of 1/3 and distance betwwen foci is 2 ?

Answer 1

Let a,b be 2 semiaxis of ellipse. Let c be distance from origin to one of the focuses.
By definition of eccentricity we have that e=c/a = 1/3.
Since distance between focuses is 2, then 2c = 2.
Then c=1 => a= c/ e = 3
Since b^2=a^2-c^2=9-1=8 we have general equation of ellipse: x^2/9 +y^2/8 = 1