Math Check
posted by Karen
Hi! Can someone check my answers? Thanks!
Questions:
1.) What are all of the foci's for this Ellipse? (x2)^2/3 + (y2)^2/4=1
A.) (3,2)
B.) (2,2)
C.) (1,2)
D.) (2,3)
E. (2,1)
My answer: B & E.
2.) What is the eccentricity for this Ellipse?
A.) 2
B.) 1/2
C.) 3/4
D. 1
My answer: A.

Reiny
a^2 = 3 , b^2 = 4
a = √3 , b = 2
so you have a vertical major axis, thus the x's must be the same , eliminating A and C
y^2 + √3 ^2 = 2^2
y^2 = 4  3 = 1
y = ± 1
so the centre is (2,2)
moving one up and one down from there gives us
(2,3) and (2,1)
e = c/b = 1/2
You should have been able to tell right away that B(2,2) could not possibly be a focus, since (2,2) is the centre
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