Concept explainers
A parabolic reflector for a car headlight forms a bowl shape that is 6 in. wide at its opening and 3 in. deep, as shown in the figure at the left. How far from the vertex should the filament of the bulb be placed if it is to be located at the focus?
To find: The distance from the vertex the filament of the bulb be placed if it is to be located at the focus.
Answer to Problem 12T
The filament of the bulb should be placed at a distance of
Explanation of Solution
Given:
The parabolic reflector for a car headlight forms a bowl shape with 6in. wide at the opening and 3 in deep.
Definition used:
“The equation of the parabola with vertex
Calculation:
Observe that from the given figure, that the parabola is open rightward, wide at the opening is 6 in and depth is 3 in.
Let the equation of the reflector be
Hence, the coordinate of the point intersects the axis and the diameter is
The points
Substitute
By the above definition, the focus of the parabola is
Since the filament of the reflector should be placed at the focus, the filament is placed at a distance of
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning