(a)
To find : An equation in standard from for the cross section of each dish if the vertex of one dish is at the origin and the vertex of the other dish is on the positive
The equation of the dish with vertex at origin is
Given information :
A person at the focus of one of two facing parabolic dishes can here even a very soft sound made at the focus of the other dish. Two such "whisper dishes" are positioned with their vertices
Formula used:
The standard form of equation of a parabola with vertex at
The standard form of the equation of a parabola with vertex
The distance
Explanation :
The vertex of one dish is at origin that is
To find the equation of the dish with vertex at origin, substitute
The vertex of the other dish is on the positive
So, the vertex of the other dish is at
To find the equation of the dish with vertex on the positive
Therefore, the equation of the dish with vertex at origin is
(b)
To calculate : The depth of each dish if the diameter of each dish is
The depth of the dish with vertex at origin is
Given information :
A person at the focus of one of two facing parabolic dishes can here even a very soft sound made at the focus of the other dish. Two such "whisper dishes" are positioned with their vertices
Calculation :
The depth of each dish if the diameter of each dish is
The dish with vertex at origin extends
Now, substitute
So, the vertex of the other dish is at
To find the equation of the dish with vertex on the positive
Therefore, the depth of the dish with vertex at origin is
(c)
To calculate : The distance between the focus and vertex for a dish that is
The distance between the focus and vertex of the given dish is
Given information :
A person at the focus of one of two facing parabolic dishes can here even a very soft sound made at the focus of the other dish. Two such "whisper dishes" are positioned with their vertices
Calculation :
The dish that is
The dish is
To calculate the distance between the focus and vertex, substitute
Therefore, the distance between the focus and vertex of the given dish is
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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