Concept explainers
To find : The standard form of the equation of parabola with the given characteristics .
Answer to Problem 34E
Explanation of Solution
Given information: Focus of parabola is at (0,0) and directrix at
Calculation:
The directrix is horizontall line .The focus lies below the directrix .The parabola always curves towards focus and away from directrix. So, this is a right downwards parabola. Therefore, the standard equation of parabola is of form
where ( h,k ) is the position of vertex of parabola and a is distance of focus from vertex.
The vertex lies exactly between the focus and directrix and must be at (0,4),so
h =0 and k =4
Since directrix and focus are 8 units apart. Therefore, vertex and focus are 4 units apart, so
a= 4
Therefore, standard equation of parabola is
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
- 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