SOLUTION: Idenitfy the equation AND the graph of the ellipse with foci at (0, +- 6) and vertices at (0, +- 8)

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Question 768411: Idenitfy the equation AND the graph of the ellipse with foci at (0, +- 6) and vertices at (0, +- 8)
Found 2 solutions by abdullahkhawer, lwsshak3:
Answer by abdullahkhawer(5) (Show Source):
You can put this solution on YOUR website!
The equation of ellipse having foci at (0,+-6) = (0,+-c) and vertices at (0,+-8) = (0,+-a) is x^2/b^2 + y^2/a^2 = 1, a > b
Also a=8,c=6 and b=√28 because c^2 = a^2 - b^2
Graph:
Foci is along y-axis because foci is at (0,+-6) which means that major axis is x=0
Let A be (0,-8) and A' be (0,8)
Let B be (-√28,0) and B' be (√28,0)
Let F be (0,-6) and F' be (0,6)
Remarks:
I hope that helped you. :)

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Identify the equation AND the graph of the ellipse with foci at (0, +- 6) and vertices at (0, +- 8)
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This is an ellipse with vertical major axis. (y-coordinates of foci and vertices change but x-coordinates do not.
Its standard form of equation: , a>b, (h,k)=(x,y) coordinates of center
For given ellipse:
y-coordinate of center=0 (midpoint of foci or vertices)
x-coordinate=0
center: (0,0)
a=8 (distance from center to vertices)
a^2=64
c=6 (distance from center to foci)
c^2=36
c^2=a^2-b^2
b^2=a^2-c^2=64-36=28
Equation:

see graph below:
y=�(64-16x^2/7)^.5