a. Together, a focus and a directrix determine a parabola. For example, can you visualize the parabola formed by the focus and directrix shown at right? Copy the focus and directrix on your paper and without folding, sketch the parabola.
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b. What is the relationship between the points on the parabola and its focus and directrix? Carefully sketch the parabola that formed on your tracing paper from problem 10-26. Mark a point on the parabola and label it P. Compare the distance between F and P to the distance between l and P. What do you notice? Does this relationship seem to hold for all points on the parabola? Explain.
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c. How does the distance between the focus (the point) and the directrix (the line) affect the shape of the parabola? Explore this by using the Focus Directrix eTool (Desmos) or tracing paper to create several parabolas with different distances between the focus and directrix. Explain the results.
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HINT: The RED Point F is the focus of the parabola. Move it up and down to see how the distance between the focus and directrix affects the shape of the parabola.
