To Find : Equations of ellipses with vertical major axes that model the largest and smallest fields described and an inequality describing the possible areas of these fields.
The equation that models the largest field is
Given information :
The playing field for Australian football is an ellipse that is between
Explanation :
From the given information, it is clear that the length of the major axis
The largest field will be the one with the largest major and minor axes lengths. So,
It is given that the ellipse has vertical major axes, so the equation of the largest field will be,
The smallest field will be the one with the smallest major and minor axes lengths. So,
It is given that the ellipse has vertical major axes, so the equation of the largest field will be,
The area of an ellipse is
Area
Area
So, the inequality representing the areas of these fields will be
Therefore, the equation that model the largest field is
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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