The equation of the ellipse having foci (4, 0), (-4, 0) and minor axis of length 16 units is:

Concept:

The distance between the centre and the focus of an ellipse is c = ae

The equation of an ellipse with the length of the major axis 2a and the minor axis 2b is given by: 

\(\rm \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\).

Calculation:

Length of the minor axis = 2b = 16.

⇒ b = 8

Also, c = distance between the centre and the focus = ae = 4.

c2 = a2e2 = a2 - b2

∴ 42 = a2 - 82

⇒ a2 = 80

Equation of the ellipse , \(\rm \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\).

⇒ \(\rm \frac{x^2}{80}+\frac{y^2}{64}=1\).