Introduction to Conics: Parabolas

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Presentation transcript:

Introduction to Conics: Parabolas Section 10.1 Introduction to Conics: Parabolas

Objective By following instructions students will be able to: Recognize a conic as the intersection of a plane and a double napped cone. How to write equations of parabolas in standard form. How to use the reflective property of parabolas to solve real life problems.

Parabolas in Real life

Circles in Real life

Ellipses in Real life

Hyperbolas in Real life

Def: Each point on any parabola is equidistant from a point called the focus and a line called the directrix. Focus lies on the axis of symmetry. Vertex lies halfway between the focus and the directrix. The directrix is perpendicular o the axis of symmetry.

Equation Focus Directrix Axis of Symmetry

EXAMPLE 1: Graph . Identify the focus, directrix, and Axis of symmetry.

EXAMPLE 2: Write an equation of a parabola whose vertex lies on the origin, and has a directrix of y=-3/2 .

U-TRY #1: Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. a) b) c) d) 2) Write the standard form of the equation of the parabola with vertex at (0,0) and the given directrix or focus. directrix: y=2 c) directrix: y=4 b) Focus (-2,0) d) focus (0,3)

EXAMPLE 3: Find the standard form of the equation of the parabola with vertex (2,1) and focus (2,4).

EXAMPLE 4: Find the focus of the parabola

EXAMPLE 5: Find the standard equation of the parabola with vertex at the origin and focus (2,0).

U-TRY #2 Find the vertex, focus, and directrix of the parabola and sketch its graph. a) b) 2) Find the standard form of the equation of the parabola with its vertex at the origin. Focus: (0, -3/2) Directrix: y=3

EXAMPLE 6: Find the equation of the tangent line to the parabola given by at the point (1,1).

Revisit Objective Did we… Recognize a conic as the intersection of a plane and a double napped cone? How to write equations of parabolas in standard form? How to use the reflective property of parabolas to solve real life problems?

Homework Pg 701 #s1-47 ODD