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# 10.2 parabolas

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### 10.2 parabolas

1. 1. Properties of Parabolas Every point on a parabola is equidistant froma point called the focus and a line called thedirectrix. The directrix isperpendicular to the lineof symmetry. The vertex is halfwaybetween the focus anddirectrix.
2. 2.  Parabolas can open vertically or horizontally.x2 = 4py y2 = 4px[Equations only good for vertex at (0, 0).]
3. 3. To Graph: Determine if the axis of symmetry is verticalor horizontal. Find and graph the focus and directrix. Solve for the squared variable, then find p. Make a table of values and plot points. Connect with a curve.
4. 4. Example: Identify the focus and directrix of theparabola given by and draw theparabola.
5. 5. Example: Identify the focus and directrix of theparabola given by and draw theparabola.
6. 6. Your Turn! Identify the focus and directrix of theparabola given by and draw theparabola.
7. 7. Writing an Equation Use the equation of the directrix to find p. Remember: y = -p or x = -p Plug that value of p into the standardequation:x2 = 4py for vertical axis of symmetryy2 = 4px for horizontal axis of symmetry
8. 8. Example: Write an equation of the parabola shown.
9. 9. Example: Write an equation of the parabola shown.
10. 10. Your Turn!Write an equation of the parabola shown.
11. 11. Parabolas in Real Life Rays that are parallel to the axis of symmetryof a parabolic reflector are all directed to thefocus. Ex: Satellite dishes Rays emitted from thefocus are reflected inrays parallel to the axisof symmetry. Ex: Flashlights
12. 12. Example: A reflector for a satellite dish is parabolic incross section, with the receiver at the focus.The reflector is 1 ft. deep and 20 ft. widefrom rim to rim. Write an equation for the cross section of thereflector. How far is the receiver from the vertex of theparabola?
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