(a)
To explain : The reason that the airplane can fly in the region bounded by the ellipse.
The sum of the distances of all the points from two fixed points called foci is constant.
Given information :
A small airplane with enough fuel to fly
Explanation :
By definition, an ellipse is the set of all the points in the plane, the sum of whose distances from two fixed points called foci is constant.
Therefore, the airplane can fly in the region bounded by the ellipse only.
(b)
To Find : The coordinates of each airport.
The coordinates of airport A is
Given information :
A small airplane with enough fuel to fly
Explanation :
The distance between airport A and airport B is
So,
Therefore, the coordinates of airport A is
(c)
To explain : The coordinates of the vertex on the basis of the distance the plane flies.
The coordinates of the vertex on the basis of the distance the plane flies are
Given information :
A small airplane with enough fuel to fly
Explanation :
As the plane flies from airport A straight past airport B to a vertex of the ellipse and then straight back to airport B.
The plane can fly maximum
Therefore, the coordinates of the vertex on the basis of the distance the plane flies are
(d)
To Find : The equation of the ellipse.
The required equation is
Given information :
A small airplane with enough fuel to fly
Explanation :
The maximum distance is
So,
Therefore, the required equation is
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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