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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
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
x2 / b2 + y2 / a2 = 1 (a > b)
Center to focus distance c = √(a2 - b2)
Foci = (0, ±c)
Vertices = (0, ± a)
The given ellipse is as shown:
Foci = (0, ±6)
Vertices = (0, ± 8)
c = √(a2 - b2)
6 = √(82 - b2)
Squaring both sides we get
36 = (64 - b2)
b2 = 64 - 36 = 28
Hence the equation of the given ellipse is :
x2 / 28 + y2 /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 x2 / 28 + y2 /64 = 1
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