Find the equation of an ellipse with the following.

$$Center: (0,0)\ Focus: (3,0)\ Vertex: (-4,0)$$

a is the distance from the origin of the ellipse c is the distance from the origin to the foci $$a = 4$$ $$c = 3$$ $$foci = (3,0), (-3,0)$$ $${b}^{2} = {a}^{2}-{c}^{2}$$ $${b}^{2} = {4}^{2}-{3}^{2}$$ $${b}^{2} = 16-9$$ $${b}^{2} = 7$$

Remember the standard form of an ellipse?

$$\frac { { x }^{ 2 } }{16} +\frac { { y }^{ 2 } }{ 7 } =1$$