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An ellipse has foci (0,-2) and (0,2) and a minor axis of lenght 6. What is the equation in standard form of the ellipse?

User Andrew Au
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Final answer:

The standard form equation of the ellipse is x^2/9 + y^2/4 = 1.

Step-by-step explanation:

The standard form equation of an ellipse with foci (0,-2) and (0,2) and a minor axis of length 6 is: x^2/9 + y^2/4 = 1.

In general, the standard form equation for an ellipse with vertical major axis is: (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) are the coordinates of the center of the ellipse, a is the length of the major axis, and b is the length of the minor axis.

In this case, the center of the ellipse is (0,0) because the foci are symmetric with respect to the x-axis. The major axis length is 2a, and the minor axis length is 2b. Since the minor axis length is given as 6, b = 3. Because the foci are located at (0,-2) and (0,2), the distance between the center and each focus is equal to a. Therefore, a = 2.

User Domos
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