5. 3 Ellipse Word Problems April 25.notebook
April 25, 2012
Graph the following. For each, state the vertices, co-vertices and foci.
1.
2.
3.
Write an equation of an ellipse with center at the origin given the following
information:
4. Vertex (4, 0); Co-vertex (0, -2)
5. Vertex: (0, -9); Focus (0, 6)
6. Co-vertex: (2, 0); Focus (0, 4)
Apr 24­12:34 PM
Apr 25­8:52 AM
Take out some paper for word problems! YAY!
Swimming Pool An elliptical pool is 20 feet long and 16 feet wide. Write an equation
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for the perimeter of the swimming pool. Assume the major axis of the pool is vertical.
Very Quick Notes:
The LENGTH of the Major Axis is equal to 2a.
The LENGTH of the Minor Axis is equal to 2b.
So, if a vertex is (0, 5), how long is the major axis?
If a co-vertex is (0, 4) how long is the minor axis?
Race Track The shape of a dirt race track for car racing is approximately an
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ellipse.The track is 400 feet long and 250 feet wide. Write an equation for the
perimeter of the race track. Assume the major axis of the track is horizontal.
Notes are done. :)
Apr 24­12:39 PM
3.
Gears In some industrial machines, elliptical gears are used instead of circular
ones. One of these elliptical gears is 12 centimeters tall and 8 centimeters wide. Write
an equation for the outline of this elliptical gear. Assume the major axis of the gear is
vertical.
Apr 24­11:41 AM
5. The train at a zoo encloses an area designed as the children's zoo. The track is in the
shape of an ellipse that is 500 yards long and 300 yards wide.
a. Write an equation of the track. Assume the major axis is horizontal.
4.
Company Logo You are in charge of designing a company logo similar to the figure
at the right. The only stipulations are that the border must be an ellipse and the width
of the ellipse must be three times the height. Write an equation in standard form for
the outline of the logo in terms of the height h.
b. The area of an ellipse is A = πab. What is the area of the children's zoo?
6. The playing field for Australian Football is an ellipse that is between
135 and 185 meters long and between 110 and 155 meters wide. Write
equations of ellipses with vertical major axes that model the LARGEST
and SMALLEST fields described.
Then, write an inequality that describes the possible areas of these
fields.
Apr 24­11:42 AM
Apr 24­12:45 PM
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5. 3 Ellipse Word Problems April 25.notebook
April 25, 2012
Patty Paper Activity: Need: graph paper, patty paper
7. A tour boat travels between two islands that are 12 miles apart. For a trip between
the islands, there is enough fuel for a 20-mile tour.
a. The region in which the boat can travel is bounded by an ellipse. Explain why this is
so.
Elliptical Pool Table: Elliptical pool tables depend on the reflective qualities of
ellipses. A ball moving across one focus point and hitting the wall of the table
will travel to a pocket located at the other focus point. Suppose you wanted to
build an elliptical pool table.
You must first construct the perfect ellipse.
The figure you have in your possess looks like an ellipse, but is it a true ellipse?
And, if the figure is a true ellipse, where would the pockets need to be located
to ensure the billiard balls follow the correct paths around the table?
b. Let (0, 0) represent the center of the ellipse. Find the
coordinates of each island.
c. Suppose the boat travels from one island, straight past the other
island to the vertex of the ellipse and back to the second island.
How many miles does the boat travel? Use your answers to find the
coordinates of the vertices.
1. Trace the ellipse on patty paper. Place this over graph paper.
2. Locate the vertical and horizontal axes of the figure and draw them on the
diagram.
3. Write an equation of the ellipse which has the axes with the measures you
found on this drawing.
4. Use your equation to find the vertices and co-vertices. Are these points on
the drawing?
5. If you believe this is an ellipse, find the foci of the diagram.
d. Write an equation of the ellipse.
Apr 24­12:49 PM
Apr 24­12:58 PM
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