This document discusses parabolas and provides examples of writing equations of and graphing parabolas given characteristics like the vertex, focus, and directrix. It defines a parabola as the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix). Examples show how to find the equation of a parabola with a given vertex and focus, graph parabolas, and solve applied problems involving the reflective properties of parabolas.

2. Sec. 9.1 ConicsObjectives: To name the Conics.

3. Sec. 9.2 The ParabolaObjectives: To find the equation to a parabola. : To graph parabolas. : To solve applied problems.ParabolaThe collection of all points P in the plane that are the same distance from a fixed point F and are from a fixed line D.Fis called the focus. D is called the directrix.

4. Parabola

5. The equation of a Parabola having a vertex @ (0, 0) and focus @ (a, 0) isEx 1 Write and graph the equation whose vertex is (0, 0) and focus is (3, 0).

6. Ex 2 Graph the equation .

7. Ex 3 Write and graph the equation whose focus is (0, 4) and directrix is y= -4.

8. Ex 4 Find the equation of the parabola with vertex at (0, 0), that contains the point , and the x-axis is the axis of symmetry.

9. Vertex (h, k)Find the equation of the parabola with vertex at (-2, 3) and the focus at (0, 3).

10. Ex 4Write and graph the equation whose focus is (2, -3) and focus is (2, -5).

11. Reflecting PropertyA satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 8 feet across at its opening and is 3 feet deep at its center, at what position should the receiver be placed?