Question 533182: How to find equation with a vertex ( 3, 0) and (13, 0) and focus ( 11, 0)?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How to find equation with a vertex ( 3, 0) and (13, 0) and focus ( 11, 0)
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Given information shows this is an equation of an ellipse with horizontal major axis of the standard form: (x-h)^2/a^2+(y-k)^2/b^2=1, a>b, with (h,k) being the (x,y) coordinates of the center.
For given equation:
x-coordinate of center=(13+3)/2=16/2=8
y-coordinate=0
center: (8,0)
..
length of major axis=13-3=10=2a
a=5
a^2=25
..
c=distance from center to focus=11-8=3
c^2=9
..
c^2=a^2-b^2
b^2=a^2-c^2=25-9=16
b=√16=4
..
Equation of given ellipse:
(x-8)^2/25+y^2/16=1
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