# Parabola with Focus and Directrix

1. Make focus at (3,-2) and equation for directrix y=7. Then click “Animate On”.
What shape does the trace make?
Review: What role does the directrix play?
Review: What role does the focus play?
Write an equation of the line or curve the trace makes. (Hint: Use equation y=a(x-h)2+k, where (h,k) is the vertex.)
Make a conjecture about how the Focus and Directrix affect the equation of a parabola.
2. Make focus at (0,0) and equation for directrix y=2. Then click “Animate On”.
Write an equation of the line or curve the trace makes. (Hint: Use equation y=a(x-h)2+k, where (h,k) is the vertex.)
Make a conjecture about how the Focus and Directrix affect the equation of a parabola.
3. Make focus at (-4,4) and equation for directrix y=0. Then click “Animate On”.
Write an equation of the line or curve the trace makes. (Hint: Use equation y=a(x-h)2+k, where (h,k) is the vertex.)
Make a conjecture about how the Focus and Directrix affect the equation of a parabola.
4. Share with your neighbor about your findings and conjecture.

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