Answer
$\frac{(x-2)^2}{7}+\frac{y^2}{16}=1$
Work Step by Step
Step 1. Identify the given quantities: ellipse center $(2,0)$, foci $(2,\pm3)$, length of major axes $8$
Step 2. As the foci are along the y-axis, we can assume a general equation as $\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$
Step 3. With the center at $(2,0)$, we have $h=2, k=0$
Step 4. The length of the major axes $2a=8$, we get $a=4$
Step 5. The distance between the foci is $2c=3+3$, we get $c=3$
Step 6. Use the relation $b^2=a^-c^2$, we get $b^2=16-9=7$
Step 7. We can write the equation for the ellipse as $\frac{(x-2)^2}{7}+\frac{(y)^2}{16}=1$
