# Write the equation of an ellipse centered at the origin with foci at (0, -3) and (0, 3) and a major axis of 10.?

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The foci are vertically aligned (they have the same x-coordinates), so the ellipse is vertical.

General equation for a vertical ellipse:

(y-k)²/a² + (x-h)²/b² = 1

with

a² ≥ b²

center (h,k)

vertices (h,k±a)

length of major axis = 2a

co-vertices (h±b,k)

foci (h,k±c), c² = a²-b²

Apply your given information and solve for h, k, a, and b.

center (h,k) = (0,0)

h = k = 0

length of major axis = 2a = 10

a = 5

foci (h,k±c) = (0,0±3)

c = 3

b² = a² - c² = 16

b = 4

The equation becomes

y²/25 + x²/16 = 1 • Login to reply the answers
• (x/4)^2+(y/5)^2=1

=>

(x^2)/16+(y^2)/25=1

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• (x/√((10/2)² - 3²))² + (y/3)² = 1

(x/4)² + (y/3)² = 1

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• The major axis lies along the y-axis, and the minor axis lies along the x-axis (because the foci are on the y-axis). The semi-minor axis is sqrt(a^2 - c^2) = 4.

x^2/16 + y^2/9 = 1.

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