with minor vertices (-3,4) and (1,4) and eccentricity=4/5
book says answer is{(x+1)^2}/4 + {(y-4)^2/100/9}=1
You should know that $\displaystyle \dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$.
Where $\displaystyle (h,k)$ is the midpoint of the axis.
Here $\displaystyle a=2$. WHY?
Using the eccentricity, how do you $\displaystyle b~?$