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Question 656908: I'm really stumped on these questions... My teachers gave me examples but I'm not sure how I can apply them into solving these:
Write the Equation of the ellipse that meet each set of conditions..
40. The foci are at (3,5) and (1,5) and the ellipse has eccentricity of 0.25
41. The ellipse has a vertical major axis of 20 units, its center is at (3,0) and e= 7/10 (eccentricity)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write the Equation of the ellipse that meet each set of conditions..
40. The foci are at (3,5) and (1,5) and the ellipse has eccentricity of 0.25
41. The ellipse has a vertical major axis of 20 units, its center is at (3,0) and e= 7/10 (eccentricity)
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40. The foci are at (3,5) and (1,5) and the ellipse has eccentricity of 0.25.
This is an ellipse with horizontal major axis.
Its standard form of equation:  , a>b, (h,k)=(x,y) coordinates of center.
For given ellipse:
center: (2,5)
length of horizontal major axis=2 (1 to 3)=2a
a=1
a^2=1
..
eccentricity=c/a=.25=1/4
c=a/4=1/4
c^2=1/16
..
c^2=a^2-b^2
b^2=a^2-c^2=1-1/16=15/16
..
Equation of ellipse:
..
41. The ellipse has a vertical major axis of 20 units, its center is at (3,0) and e= 7/10 (eccentricity)
This is an ellipse with vertical major axis as stated
Its standard form of equation:  , a>b, (h,k)=(x,y) coordinates of center.
For given ellipse:
center: (3,0)
length of vertical major axis=20=2a
a=10
a^2=100
..
eccentricity=c/a=7/10
c=7a/10=7
c^2=49
..
c^2=a^2-b^2
b^2=a^2-c^2=100-49=51
..
Equation of ellipse:
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