Final answer:
These word problems related to conic sections provide practice in applying analytic and computational concepts to scenarios involving parabolic mirrors, elliptical orbits, and conic cross-sections.
Step-by-step explanation:
Conic sections are curves that can be formed by the intersection of a plane with a cone, including circles, ellipses, parabolas, and hyperbolas. Here are a few word problems related to conic sections:
Word Problem 1: Parabolic Mirror
A satellite dish is built in the shape of a parabola and is designed to focus signals at the dish's focal point, where the receiver is located. If the dish has a diameter of 10 feet and is 2.5 feet deep at its center, where is the focal point located relative to the vertex of the parabola?
Word Problem 2: Orbit of a Planet
An elliptical orbit of a planet around the sun shows the sun at one focal point of the ellipse. If the maximum distance of the planet from the sun is 150 million kilometers and the minimum distance is 100 million kilometers, what is the eccentricity of the orbit?
Word Problem 3: Cross-Section of a Cone
A cone with height 12 cm and base radius 5 cm is cut with a plane parallel to its base 3 cm from the top. What shape is the cross-section, and what are the dimensions?
These problems give students additional practice working with the analytic and computational concepts of conics in precalculus, integrating mathematics and other disciplines to deepen understanding of physical phenomena.