SOLUTION: Find the equation of the ellipse whose length of the major axis is 20 and foci are (0, ±5)

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Question 632529: Find the equation of the ellipse whose length of the major axis is 20 and
foci are (0, ±5)
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the equation of the ellipse whose length of the major axis is 20 and
foci are (0, ±5)
**
This is an ellipse with vertical major axis.
Its standard form of equation: %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1
center:(0,0)
2a=length of vertical major axis=20
a=10
a^2=100
..
distance between foci=10=2c
c=5
c^2=25
..
c^2=a^2-b^2
b^2=a^2_c^2=100-25=75
b=√75≈8.7
..
Equation of given ellipse:
x%5E2%2F75%2By%5E2%2F100=1