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Question 546677: Write the equation of the ellipse centered at the origin given a focus (0,2) and a vertex (0,3).
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write the equation of the ellipse centered at the origin given a focus (0,2) and a vertex (0,3).
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Since the y-coordinates of the focus and vertex differ while the x-coordinates do not, this is an ellipse with vertical major axis. Its equation of standard form:
(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, with (h,k) being the (x,y) coordinates of the center.
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For given ellipse:
Center: (0,0) (given)
length of vertical major axis=6=2a
a=3
a^2=9
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2c=4
c=2
c^2=4
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c^2=a^2-b^2
b^2=a^2-c^2=9-4=5
b=√5≈2.24
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Equation of given ellipse:
(x-h)^2/b^2+(y-k)^2/a^2=1
(x-0)^2/5+(y-0)^2/9=1
x^2/5+y^2/9=1 (ans)
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