Sec. 9.2 The Parabola Objectives: To find the equation to a parabola. : To graph parabolas. : To solve applied problems. Parabola The 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.
The equation of a Parabola having a vertex @ (0, 0) and focus @ (a, 0) is Ex 1 Write and graph the equation whose vertex is (0, 0) and focus is (3, 0).
Ex 2 Graph the equation .
Ex 3 Write and graph the equation whose focus is (0, 4) and directrix is y= -4.
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.
Vertex (h, k) Find the equation of the parabola with vertex at (-2, 3) and the focus at (0, 3).
Ex 4Write and graph the equation whose focus is (2, -3) and focus is (2, -5).
Reflecting Property A 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?