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# Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -6), (0, 6); Vertices: (0, -8), (0, 8)

**Solution:**

When the focii are on the y-axis the general equation of the ellipse is given by

x^{2 }/ b^{2} + y^{2 }/ a^{2} = 1 (a > b)

Center to focus distance c = √(a^{2} - b^{2})

Foci = (0, ±c)

Vertices = (0, ± a)

The given ellipse is as shown:

Foci = (0, ±6)

Vertices = (0, ± 8)

c = √(a^{2} - b^{2})

6 = √(8^{2} - b^{2})

Squaring both sides we get

36 = (64 - b^{2})

b^{2} = 64 - 36 = 28

Hence the equation of the given ellipse is :

x^{2 }/ 28 + y^{2} /64 = 1 (a > b)

## Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -6), (0, 6); Vertices: (0, -8), (0, 8)

**Summary:**

The standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -6), (0, 6); Vertices: (0, -8), (0, 8) is x^{2 }/ 28 + y^{2} /64 = 1

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