Answer:
x squared over 4 plus and squared over 8 equals 1, x^2/4 + y^2/8 = 1
Step-by-step explanation:
We have that the general ellipse equation is as follows:
x^2/a^2 + y^2/b^2 = 1
Furthermore, the foci is (0, c) and b> a we have to:
c ^ 2 = b ^ 2 - a ^ 2
However,
guideline x = + - b / e and foci (0, + - ab)
where is e is the eccentricity, therefore:
b / e = 4, then e = b / 4
and we also have b * e = 2, we replace:
b * (b / 4) = 2
b ^ 2 = 8
replacing:
2 ^ 2 = 8 - a ^ 2
a ^ 2 = 8 - 2 ^ 2
a ^ 2 = 8 - 4
a ^ 2 = 4
Therefore if we replace in the general equation it would be
x^2/4 + y^2/8 = 1
that is, x squared over 4 plus and squared over 8 equals 1
