- The information that can be obtained from the given diagram.
- The information needed to be able to write an equation that models the cross section of the mirror.
The information that can be obtained from the given diagram and the additional information needed to write an equation that models the cross section of the mirror have been provided.
Given:
The diagram showing a mirror with a parabolic cross section, which is used to concentrate sunlight on a pipe, located at the focus of the mirror; as follows:
  
Concept used:
An equation of a parabola can be written with the help of at least two of the three information: coordinates of vertex, coordinates of focus and equation of directrix.
Calculation:
It can be seen from the given diagram that the distance between the vertex and focus of the parabola to be modelled, is
In fact, this is the only information that can be obtained from the given diagram.
It should be noted that neither the coordinates of the vertex nor the coordinates of the focus can be obtained from this information, both of which are needed to write the equation of the parabola.
Hence, additional information is needed in the form of coordinates of the vertex or coordinates of the focus or equivalently, a
Conclusion:
The information that can be obtained from the given diagram and the additional information needed to write an equation that models the cross section of the mirror have been provided.
Chapter 10 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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