Graph the ellipse with equation x squared divided by 4 plus y squared divided by 49 = 1

Question

Graph the ellipse with equation x squared divided by 4 plus y squared divided by 49 = 1

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    0
    2021-10-11T04:30:58+00:00

    \frac{x^2}{4} +\frac{y^2}{49} =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 = 4  so b= 2

    a^2 = 49 so a = 7

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

    c=\sqrt{49 -4}=3\sqrt{5}

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

    We know h=0  , k=0  and a= 7

    Vertices are (0,-7)  and (0,7)

    Foci are (h, k+c)  and (h,k-c)

    We know h=0  , k=0  and c=3\sqrt{5}

    Foci are (0,-3\sqrt{5})  and (0,3\sqrt{5})

    0
    2021-10-11T04:31:13+00:00

    Answer with Step-by-step explanation:

    We have to graph the ellipse:

    \dfrac{x^2}{4}+\dfrac{y^2}{49}=1

    when x=0 , \dfrac{y^2}{49}=1

    i.e. y²=49

    i.e. y= ±7

    ellipse passes through (0,7) and (0,-7)

    when y=0, \dfrac{x^2}{4}=1

    i.e. x² = 4

    i.e. x= ± 2

    i.e. ellipse passes through (2,0) and (-2,0)

    The ellipse is shown as below:

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