Final answer:
The statement is false. A hyperbolic border is usually associated with a mirror, not a lens. The vertices represent the points where the mirror curves the most, and the foci represent the points where parallel rays would intersect after reflecting off the mirror.
Step-by-step explanation:
The statement is false.
In optics, a hyperbolic border is usually associated with a mirror, not a lens. Since the question mentions a lamp and a hyperbolic border, it is more likely referring to a curved mirror. The vertices of the hyperbolic border represent the points where the mirror curves the most, and the foci represent the points where parallel rays would intersect after reflecting off the mirror. In this case, the vertices are 18 inches apart and the foci are 5 inches apart.