Final answer:
A hyperbolic mirror is used in a reflecting telescope, which eliminates chromatic aberration and focuses light using reflection rather than refraction. Reflecting telescopes are common in both amateur and professional astronomy.
Step-by-step explanation:
A telescope being built with a hyperbolic mirror contributes to a reflecting telescope system. Telescopes that use mirrors as their main optical elements, such as the hyperbolic ones in question, rely on reflection rather than refraction to form images. These telescopes, including notable designs like the Newtonian and Cassegrain, have a primary mirror with a shiny metal coating that reflects light to a focal point. Unlike refracting telescopes, which suffer from chromatic aberration due to lens refraction, reflecting telescopes entirely avoid this issue and are the most common type among both amateur and professional astronomical instruments. The first successful reflecting telescope was built by Isaac Newton in 1668, showcasing the practicality and effectiveness of the design. Therefore, the correct answer for a hyperbolic mirror used in a telescope is a reflecting telescope, indicated by option B.