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Value of p:
The equation of the ellipse is:
$4x^2 + py^2 = 80$
Since it passes through the points $(0, \pm 4)$:
$4(0)^2 + p(\pm 4)^2 = 80$
$16p = 80 \implies p = 5$

Standard Equation of the Ellipse:
Substituting $p = 5$ into the equation:
$4x^2 + 5y^2 = 80$
Dividing both sides by 80:
$\frac{x^2}{20} + \frac{y^2}{16} = 1$
Here, $a^2 = 20 \implies a = 2\sqrt{5}$ and $b^2 = 16 \implies b = 4$.
Since $a > b$, the major axis lies along the x-axis.

Eccentricity (e):
$e = \sqrt{1 - \frac{b^2}{a^2}} = \sqrt{1 - \frac{16}{20}} = \sqrt{\frac{4}{20}} = \frac{1}{\sqrt{5}}$

Coordinates of the Foci:
$\text{Foci} = (\pm ae, 0) = \left(\pm 2\sqrt{5} \cdot \frac{1}{\sqrt{5}}, 0\right) = (\pm 2, 0)$

Lengths of the Axes:

• Length of major axis $= 2a = 2(2\sqrt{5}) = 4\sqrt{5}$ units
• Length of minor axis $= 2b = 2(4) = 8$ units