Calculus homework answer?

Identify and choose the appropriate quadric surface. (choices in the picture attached)

Choices:A.) Figure 4. Hyperboloid of one sheet

B.) Figure 5. Ellipsoid

C.) Figure 2. Hyperboloid of two sheets.

D.) Figure 1. Hyperboloid of one sheet.

E.) Figure 3. Ellipsoid.

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  • 1 month ago
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    B) Figure 5. Ellipsoid

    Explanation:

    Equation 

    x^2 / a^2 + y^2 / b^2 + z^2 / c^2 = 1

    is equation of an ellipsoid.

    So which one is it, Figure 3 or Figure 5?

    In this general equation, a, b and c are half the length of the principal axes in x, y and z direction, respectively.

    In our case, a=1, b=8, c=16, so the ellipsoid is elongated in z-direction. From picture, that is Figure 5.

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