# If the length of major and semi-minor axis of an ellipse are $8 , 2$ and their corresponding equations are $y-6=0$ and $x+4=0$ then the equations of the ellipse is

$\begin{array}{1 1}(1)\large\frac{(x+4)^{2}}{4}+\frac{(y-6)^{2}}{16}=1&(2)\frac{(x+4)^{2}}{16}+\frac{(y-6)^{2}}{4}=1\\(3)\frac{(x+4)^{2}}{16}-\frac{(y-6)^{2}}{4}=1&(4)\frac{(x+4)^{2}}{4}-\frac{(y-6)^{2}}{16}=1\end{array}$

Length of major axis $2a=8 => a=4$
Length of semi minor axis $b=2$
Equation of major axis $y-6=0$
Equation of minor axis $x+4=0$
$\therefore$ The equation of the ellipse is
$\frac{(x+4)^{2}}{16}+\frac{(y-6)^{2}}{4}=1$
Hence 2 is the correct answer.