Yahoo Answers: Answers and Comments for What are the vertices, covertices, and foci of the ellipse (x5)^2/64 + (y10)^2/100 = 1? [Mathematics]
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From Anonymous
enUS
Wed, 22 May 2019 00:48:19 +0000
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Yahoo Answers: Answers and Comments for What are the vertices, covertices, and foci of the ellipse (x5)^2/64 + (y10)^2/100 = 1? [Mathematics]
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From DWRead: (x5)²/64 + (y10)²/100 = 1
The denominator of...
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Wed, 22 May 2019 01:14:21 +0000
(x5)²/64 + (y10)²/100 = 1
The denominator of the y term is larger than the denominator of the x term, so the ellipse is vertical.
General equation for a vertical ellipse:
(yk)²/a² + (xh)²/b² = 1
with
a ≥ b
center (h,k)
vertices (h,k±a)
covertices (h±b,k)
foci (h,k±c), c² = a²b²
(y10)²/10² + (x5)²/8² = 1
center (5,10)
vertices (5,10±10) = (5,20) and (5,0)
covertices (5±8,10) = (13,10) and (3,10)
c = √(10²8²) = 6
foci (5,10±6) = (5,16) and (5,4)

From Anonymous: a = 5, b = 4
c^2 = 2516 = 9
c = ±3
Centre = ...
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Wed, 22 May 2019 02:44:36 +0000
a = 5, b = 4
c^2 = 2516 = 9
c = ±3
Centre = (5,10)
Vertices = (5,0), (5,20)
Covertices = (3,10), (13,10)
Foci (5,13),(5,7)

From Φ² = Φ+1: ((x5)/8)^2 + ((y10)/10)^2 = 1
Vertices (Majo...
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Wed, 22 May 2019 00:57:07 +0000
((x5)/8)^2 + ((y10)/10)^2 = 1
Vertices (Major axis): (5,1010)=(5,0) and (5,10+10)=(0,20)
Covertices (Minor axis): (58,10)=(3,10) and (5+8,10)=(13,10)
Foci: (5,10√(10²8²))=(5,4) and (5,10+√(10²8²))=(5,16)

From alex: (xh)^2/a^2+ (yk)^2/b^2 = 1 , with a<b
the...
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Wed, 22 May 2019 00:54:03 +0000
(xh)^2/a^2+ (yk)^2/b^2 = 1 , with a<b
the vertices (h , kb) and (h , k+b)
covertices (ha , k) and (h+a , k)
foci (h , hc) and (h , h+c) , with c = √(b^2  a^2)