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6 August, 10:14

Find the equation of the ellipse with the following properties:

Vertices at (-6,-3) and (0,-3)

e=1/3

+2
Answers (1)
  1. 6 August, 11:24
    0
    Answer: The equation of an ellipse:

    (

    x

    -

    h

    )

    2

    a

    2

    +

    (

    y

    -

    k

    )

    2

    b

    2

    =

    1

    ;

    a

    >

    b

    Has vertices at

    (

    h

    ±

    a

    ,

    k

    )

    Has foci at

    (

    h

    ±



    a

    2

    -

    b

    2

    ,

    k

    )

    Use the vertices to write 3 equations:

    k

    =

    4

    [1]

    h

    -

    a

    =

    -

    6

    [2]

    h

    +

    a

    =

    10

    [3]

    Use equations [2] and [3] to solve for h and a:

    2

    h

    =

    4

    h

    =

    2

    a

    =

    8

    Use the focus to write another equation:

    8

    =

    h

    +



    a

    2

    -

    b

    2

    Substitute values for h and a:

    8

    =

    2

    +



    8

    2

    -

    b

    2

    6

    =



    64

    -

    b

    2

    36

    =

    64

    -

    b

    2

    b

    2

    =

    64

    -

    36

    b

    2

    =

    28

    b

    =



    28

    Substitute the values into the standard form:

    (

    x

    -

    2

    )

    2

    8

    2

    +

    (

    y

    -

    4

    )

    2

    (



    28

    )

    2

    =

    1
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