Answer
See below
Work Step by Step
The vertex is with coordinates $(7,0)=(\pm a,0) \rightarrow a=\pm 7$
The focus is with coordinates $(-3,0)=(\pm c,0) \rightarrow c=\pm 3$
Finding b, we obtain: $c^2=a^2-b^2\\(\pm 3)^2=(\pm 7)^2-b^2\\9=49-b^2\\b^2=40$
The standard equation for an ellipse:
$$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$$
Substitute:$$\frac{x^2}{(\pm 7)^2}+\frac{y^2}{40}=1\\ \frac{x^2}{49}+\frac{y^2}{40}=1$$
