Find the center, vertices, and foci of the ellipse with equation x squared divided by 36 plus y squared divided by 100 = 1

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Find the center, vertices, and foci of the ellipse with equation x squared divided by 36 plus y squared divided by 100 = 1

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    2021-10-11T04:10:10+00:00

    \frac{x^2}{36} +\frac{y^2}{100} =1

    General equation is

    \frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1

    Where (h,k) is the center

    From the given equation h=0  and k=0

    So center is (0,0)

    compare the given equation with general equation

    b^2 = 36  so b= 6

    a^2 = 100 so a = 10

    c=\sqrt{a^2 -b^2}

    c=\sqrt{100 -36}= 8

    Vertices are (h, k+a) and (h, k-a)

    We know h=0  , k=0  and a= 10

    Vertices are (0,-10)  and (0,10)

    Foci are (h, k+c)  and (h,k-c)

    We know h=0  , k=0  and c=8

    Foci are (0,-8)  and (0,8)

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