# Parabola with Focus and Directrix

Topic:
Parabola
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.