Problema Solution
an ellipse has eccentricity of 1/3. find the distance between 2 directrix if the distance between foci is 3.
Answer provided by our tutors
Focal Distance of a Point:
To find the distance of any point on the ellipse from the focus, we use the definition of the ellipse.
Let P(x, y) be a point on the ellipse. Then
S¢P = ePN¢ = e(a/e -x) = a - ex
SP = ePN = e ( a/e + x) = a + ex
S¢P + SP = 2a
Distance between the foci = 2ae = 3
e = eccentricity = 1/3
--> 2a(1/3) = 3
--> 2a = 9
--> a = 9/3 = 3