Final answer:
To find the equation for an ellipse given the focus and vertices, we need to know the location of the center. In this case, the center is at (25,0). The equation of the ellipse is (x-25)^2/0.5^2 + y^2/0.5^2 = 1.
Step-by-step explanation:
To find the equation for an ellipse given the focus and vertices, we need to know the location of the center. Since the focus is at (24,0) and the vertices are at (+26,0), the center must be halfway between these points, which is at (25,0).
The distance between the center and each vertex is called the semi-major axis and it equals half of the distance between the vertices. In this case, the semi-major axis is (26-25)/2 = 0.5.
Since the ellipse is centered at (25,0), the equation of the ellipse is (x-25)^2/a^2 + y^2/b^2 = 1, where a is the length of the semi-major axis and b is the length of the semi-minor axis. Since the semi-minor axis is equal to the semi-major axis, the equation can be simplified to (x-25)^2/0.5^2 + y^2/0.5^2 = 1.
Now, we can graph the equation using these values.