SOLUTION: find the equation of the ellipse , eccentricity = 4/5 , a centre at (0,0) and foci (+-8,0)

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Question 752402: find the equation of the ellipse , eccentricity = 4/5 , a centre at (0,0) and foci (+-8,0)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You want to fill in x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1 with the particular values. Center is at the origin so no need to worry about x and y translation. The focal distance according to your given foci is c=8.

If eccentricity is 4/5, then you have 4%2F5=c%2Fa. You can find a.
a%2Fc=5%2F4
a=5c%2F4=5%2A8%2F4=highlight%2810%29

Next, find b. a%5E2=b%5E2%2Bc%5E2
b%5E2=a%5E2-c%5E2
You do not quite need b for filling in that part of the equation but you still have the value in the form of its square. b%5E2=10%5E2-8%5E2=100-64=highlight%2836%29

Equation is highlight%28x%5E2%2F64%2By%5E2%2F36=1%29