Question 424765: Write the equation of the conic section with the given characteristics. Ellipse. Vertices at (4,-9) and (4,7) and Foci at (4,-6) and (4,4)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write the equation of the conic section with the given characteristics. Ellipse. Vertices at (4,-9) and (4,7) and Foci at (4,-6) and (4,4)
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Based on given data, this is an ellipse with vertical major axis on x=4.
Standard form for this ellipse: (y-k)^2/a^2+(x-h)^2/b^2=1 (a>b)
The x-coordinate of center=4
The y-coordinate of center=7+(-9)/2=-2/2=-1
Center,therefore, is at (4,-1)
2a=length of major axis=16
a=8
a^2=64
c=5=distance from center on major axis,(y=-1) to either of given foci points(4,-6) or (4,4)
c^2=a^2-b^2
b^2=a^2-c^2=64-25=39
b=sqrt(39)=6.24..(1/2 minor axis)
Equation:
(y+1)^2/64+(x-4)^2/39=1
See the graph of the ellipse below:
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y=+-((64-64(x-4)^2/39)^.5)-1
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