Determining an equation

Question

Use the given information about the graph of an ellipse to determine its equation.

center at the origin, symmetric with respect to the x- and y-axes, focus at (4, 0),

 and point on graph (0, 3)

Answer 1

The ellipse is oriented with the major axis in x direction and foci at (4,0) and (-4,0). The focal length, c, is 4. The point (0,3) lies on the minor axis (b = 3). The major axis, a, is obtained from a² = b² + c² (a = 5)

The equation is x²/5² + y²/3² = 1