Correct Answer - Option 1 :
\(\rm \frac{x^2}{80}+\frac{y^2}{64}=1\)
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 = \(\rm \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\).
⇒ \(\rm \frac{x^2}{80}+\frac{y^2}{64}=1\).
