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March 05, 2012
Students explore two different methods for constructing an ellipse.
Students use a perpendicular line to a segment FP. FP connects two points F and P where P is a point that lies on the circumference of a circle and F is a fixed point also known as the focus, which lays on the diameter.
Students use the Locus command in Cabri™ Jr. to generate an outline of an ellipse. The ellipse is formed by an envelope of lines hence the method’s name.
Students will see that the diameter of the circle is equal to the width of the ellipse along its longer axis also called the major axis. They will notice that the focus can be used to construct the ellipse.
Then, students explore a second method called String and Pins Construction. They use the definition of an ellipse to construct it.
At the end of this activity, students will be able to derive the equation of an ellipse in rectangular form and write an equation of an ellipse with the center at (0, 0) given its vertices and co-vertices. They will also know two methods of constructing an ellipse.
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