Question 143417: Consider the ellipse whose equation is (x-3)^2/ 25 + (y-4)^2/16 =1
a. what is the center? (3,4)?
b. What are the lenghts of the major and minor axes, and the distance between the foci?
c. find the coordinates of the focal points.
thank you so much
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Consider the ellipse whose equation is (x-3)^2/ 25 + (y-4)^2/16 =1
a. what is the center?...... (3,4)
b. What are the lengths of the major and minor axes,
Major: Vertices are (3-5,4) and (3+5,4) or (-2,4) and (8,4)
So the length of the major axis is 8--2 = 10 units.
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Minor: Co-vertices are (3,4-4) and (3,4+4) or (3,0) and (3,8)
So the length of the minor axis is 8-0 = 8 units
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and the distance between the foci?
a=5, b=4, so c=sqrt(25-16) = 3
So distance between the foci is 2*3 = 6
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c. find the coordinates of the focal points.
(3-3,4) and (3+3,4) or (0,4) and (6,4)
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Cheers,
Stan H.
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