SOLUTION: (0,0)(0,8);12 FIND THE EQUATION OF THE ELLIPSE GIVEN THE FOLLOWING POINTS AS FOCI AND THE GIVEN NUMBER AS A SUM OF THE FOCAL RADII

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: (0,0)(0,8);12 FIND THE EQUATION OF THE ELLIPSE GIVEN THE FOLLOWING POINTS AS FOCI AND THE GIVEN NUMBER AS A SUM OF THE FOCAL RADII       Log On


   

Question 887587: (0,0)(0,8);12 FIND THE EQUATION OF THE ELLIPSE GIVEN THE FOLLOWING POINTS AS FOCI AND THE GIVEN NUMBER AS A SUM OF THE FOCAL RADII
Answer by lwsshak3(11628) About Me  (Show Source):
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(0,0)(0,8);12 FIND THE EQUATION OF THE ELLIPSE GIVEN THE FOLLOWING POINTS AS FOCI AND THE GIVEN NUMBER AS A SUM OF THE FOCAL RADII
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Given ellipse has a vertical major axis.
Its standard form of equation: %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1, a>b, (h,k)=coordinates of center
..
center:(0,4)
Sum of focal radii=12=2a
a=6
a^2=36
c=4 (distance from center to foci)
c^2=16
c^2=a^2-b^2
b^2=a^2-c^2=36-16=20
equation: x%5E2%2F20%2B%28y-4%29%5E2%2F36=1