Question 579458: write an equation for each ellipse described: the major axis has endpoints at (-3,4) and (13,4) and is parallel to the axis; the foci are at (5-sqrt ( 55 ),4) and (5+sqrt (55 ),4) ?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! write an equation for each ellipse described: the major axis has endpoints at (-3,4) and (13,4) and is parallel to the axis; the foci are at (5-sqrt ( 55 ),4) and (5+sqrt (55 ),4) ?
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Standard form of equation for an ellipse with horizontal major axis:
(x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k) being the (x,y) coordinates of the center.
For given ellipse:
x-coordinate of center=(-3+13)/2=5 (use midpoint formula)
y-coordinate=4
center=(5,4)
length of horizontal major axis=16=2a
a=8
a^2=64
..
c=√55≈7.42(given)
c^2=55
..
c^2=a^2-b^2
b^2=a^2-c^2=64-55=9
..
Equation for given ellipse:
(x-5)^2/64+(y-4)^2/9=1
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