Math Check

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Hi! Can someone check my answers? Thanks!



Questions:

1.) What are all of the foci's for this Ellipse? (x-2)^2/3 + (y-2)^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.

  • Math Check -

    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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