What you have here is the equation of an ellipse.
The general form is
The center of the ellipse is (0, 0).
The direction of the major axis is horizontal.
The length of the major axis is 2a.
The length of the minor axis is 2b.
An ellipse has two axes of symmetry which contain the major and minor axes. The lengths a, b, and c are related by the formula:
Using a = 4 and b = 3, find c.
The foci are at (-c, 0) and (c, 0).
The vertices of the major axis are at (-a, 0) and (a, 0). These are also your x-intercepts.
The vertices of the minor axis are at (0, b) and (0, -b).
These are also your y-intercepts.
You now have enough information to graph the ellipse.