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Foci (0,-3)(0,3)

Vertices (0,-4)(0,4)
Find the standard form

1 answer

Foci: (0,-3) (0,3).
Vertices: (0,-4) (0,4).

The X-coordinate of the Foci and Vertices are constant at zero while the
Y-coordinates varies. Therefore, we have a y-Elipwse. So a^2 will be located under Y^2:

X^2/b^2 + Y^2/a^2 = 1.

a^2 = 4^2 = 16.

F^2 = a^2 - b^2 = 3^2,
16 - b^2 = 9,
b^2 = 7.
b = sqrt7.

Eq: X^2/7 + y^2/16 = 1.