Advanced Precalculus Notes 9.2 Introduction to Conics: Parabolas Definition of a parabola: The set of all points (x, y) that are equidistant from a line.

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Advanced Precalculus Notes 9.2 Introduction to Conics: Parabolas Definition of a parabola: The set of all points (x, y) that are equidistant from a line (directrix) and a point (focus) not on the line. Parabaloid: Three dimensional rotation of a parabola.

Standard form of a parabola, vertex at the origin:vertex (0, 0) focus (p, 0)focus (0, p) directrix: x = - pdirectrix: y = - p Find the vertex, focus and directrix of each parabola:

Standard form of a parabola, vertex at (h, k) vertex (h, k) focus (h + p, k)focus (h, k + p) directrix: x – h = - pdirectrix: y – k = - p x = h – p y = k – p Graphs: p > 0p 0p < 0

Find an equation of the parabola with vertex at (-2, 3) and focus at (0, 3).

Find the focus, vertex, directrix and graph of:

Completing the square: Find the focus, vertex, directrix and graph of :

A satellite dish is shaped like a paraboloid of revolution. It the dish is 8 feet across at its opening and 3 feet deep at its center, at what position should the receiver be placed?

Find the focus, vertex, directrix and graph of:

Assignment: page 661: 1 – 18, 19, 27, 29, 39, 47, 57, 63, 67, 73