10.2 Parabolas JMerrill, 2010. Review—What are Conics Conics are formed by the intersection of a plane and a double-napped cone. There are 4 basic conic.

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10.2 Parabolas JMerrill, 2010

Review—What are Conics Conics are formed by the intersection of a plane and a double-napped cone. There are 4 basic conic sections. Notice that the plane does not pass through the vertex. If that happens, the resulting figure is a degenerate conic…

Degenerate Conics

Definition of the Parabola A parabola is the set of all points (x, y) in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.

Equations See p. 736

Orientation State the direction in which each parabola opens (the orientation). a) b) c) d) left down up right

Example: Find the coordinates of the vertex and focus, the equation of the directrix, and graph the parabola orientation: up vertex: (2, -3) Focus—find p (2, -2.5) directrix: y = -3.5 You will need to graph it in order to find how wide the parabola opens

You Try orientation: right vertex: (0, 5) focus: (.25, 5) directrix: x = -.25

Finding the Equation Find the standard form of the equation of the parabola with vertex (2, 1) and focus (2, 4) Draw what you know Is the axis of symmetry vertical or horizontal? So the model is (x - h) 2 = 4p(y – k) What is p? Equation? 3 (x - 2) 2 = 12(y – 1)