Question 413064: Determine the standard equation of the ellipse given:
Center: (3,4) Focus (8,4) Also contains the point: (3,8) Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Determine the standard equation of the ellipse given:
Center: (3,4) Focus (8,4) Also contains the point: (3,8)
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Standard form of given ellipse:
(x-3)^2/a^2+(y-4)^2/b^2=1
c=distance from ctr to focus on major axis=5
c^2=a^2-b^2
25=a^2-b^2
b^2=a^2-25
Using point on ellipse (3,8)
(3-3)^2/a^2+(8-4)^2/b^2=1
0+4^2/b^2=1
b^2=16
a^2=c^2+b^2=25+16=41
equation of ellipse:
(x-3)^2/41+(y-4)^2/16=1
see graph below:
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y=4+((656-16(x-3)^2)/41)^.5
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