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Hello,
If center is (0,0)
x²/a²+y²/b²=1 for a half horizontal axis of a, and a half vertical axis of b
Here
a=2 ==> a²=4
b=8 ==> b²=64
[tex]\boxed{\dfrac{x^2}{4}+ \dfrac{y^2}{64}=1}\\[/tex]