Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)

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Solution

Length of minor axis = 16; foci = (0, ±6).

Since the foci are on the y-axis, the major axis is along the y-axis.

Therefore, the equation of the ellipse will be of the form, where a is the semi-major axis.

Accordingly, 2b = 16 ⇒ b = 8 and c = 6.

It is known that.

Thus, the equation of the ellipse is.

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