SOLUTION: 1. The equation of an ellipse is given by (x-3)^2/64 + (y+5)^2/100 = 1 a. Identify the coordinates of the center of the ellipse. b. Find the length of the major and minor axes

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 1. The equation of an ellipse is given by (x-3)^2/64 + (y+5)^2/100 = 1 a. Identify the coordinates of the center of the ellipse. b. Find the length of the major and minor axes      Log On


   



Question 453957: 1. The equation of an ellipse is given by (x-3)^2/64 + (y+5)^2/100 = 1
a. Identify the coordinates of the center of the ellipse.
b. Find the length of the major and minor axes.
c. Find the coordinates of the foci.
d. Graph the ellipse. Label the center and foci.

Answer by Alan3354(69443) About Me  (Show Source):
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The equation of an ellipse is given by (x-3)^2/64 + (y+5)^2/100 = 1
a. Identify the coordinates of the center of the ellipse.
(x-3)^2/64 + (y+5)^2/100 = 1 the form is %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1
The center is (3,-5)
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b. Find the length of the major and minor axes.
The semi-major axis = sqrt(b^2) = 10 --> major axis = 20 (vertical)
Minor axis = 16
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c. Find the coordinates of the foci.
The distance from the center = sqrt%28b%5E2-a%5E2%29+=+sqrt%28100-64%29+=+6
6 is added and subtracted from the y values.
--> (3,1) and (3,-11)
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d. Graph the ellipse. Label the center and foci.
dl the FREE graph software at
http://www.padowan.dk
Use F6 to enter the function as it is.