Concept explainers
To find: the equation of the parabola.
Answer to Problem 49E
The equation of parabola is
Explanation of Solution
The equation of parabola is
Given information:
From the given figure it can be observed that,
The graph of the parabola opens to the downwards and parabola has vertical axis.
The shaded region area is
Calculation:here, the graph of parabola opens to the downwards, so
Because the parabola has vertical axis,
So the equation of parabola should be in the following form,
Area of shaded region area =
The shaded region is rectangle.
So the area of each rectangle made by rectangle =
So it is shown that the width of the rectangle is two times of length of the rectangle.
So,
The length of the rectangle is equal to the distance of focus from the origin.
So the focus is
So,
So the equation of parabola is,
Hence, the equation of parabola is
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning