Focus of a Parabola Section 2.3 beginning on page 68.

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Presentation transcript:

Focus of a Parabola Section 2.3 beginning on page 68

By the End of This Section You will understand how a parabola is related to it’s focus and directrix. You will understand how the focus and directrix affect the shape of a parabola. You will be able to write an equation for a parabola with the vertex on the origin when given its focus or directrix. You will be able to identify the focus, directrix, and axis of symmetry given the equation of a parabola that has it’s vertex at the origin.

The Focus and Directix

A Parabola With Vertex (0,0) A parabola with a vertex (0,0) that opens up or down, has a focus (0,p), and a directrix y=-p has the equation : A parabola with a vertex (0,0) that opens left or right, has a focus (p,0), and a directrix x=-p has the equation :

Axis of sym is the x-axis Step 3: Find two points one side of the axis of sym, then reflect them to the other side of the axis of sym.

Substitute that value of p into the general equation and simplify..

Quick Practice

Because the vertex is at the origin, and the axis of symmetry is vertical, the equation is of the form … The engine is at the focus, which is 4.5 meters above the vertex, so … Use p to write the equation. The depth of the dish is the y-value at the edge of the dish. That x value will be half of the width of the dish since the dish is centered on the origin. The depth of the dish is about 1 meter.

Quick Practice The antenna is 1.6 feet deep.