Answer:
[tex]\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]
Step-by-step explanation:
If the ellipse has its x-intercepts at points (2, 0) and (-2, 0) and y-intercepts at points (0, 4) and (0, -4), then its symmetric across the y-axis and across the x-axis.
Moreover,
[tex]a=2\\ \\b=4[/tex]
The equation of such ellipse is
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
Hence, the equation of the ellipse is
[tex]\dfrac{x^2}{2^2}+\dfrac{y^2}{4^2}=1\\ \\ \\\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]
