Question

Eccentricity of 16x^2 +64y^2-1024=0

Answer 1

16x^2 +64y^2-1024=0

16x^2 +64y^2 = 1024
divide by 1024

x^2/64 + y^2/16 = 1

you are looking at at ellipse with a = 8 and b = 4

In an ellipse in standard position like yours
c^2 = a^2 - b^2 = 64-16 = 48
c = √48 = 4√3

e = c/a = 4√3/8 = √3 / 2