11.3 PARABOLAS Directrix (L): A line in a plane.

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Presentation transcript:

11.3 PARABOLAS Directrix (L): A line in a plane. Focus (P): A point NOT on the directrix. X is any point on the parabola

Axis: The line through the focus P ⊥ to the directrix L. Vertex: The intersection of the axis with the parabola (midpoint of P to L). Equation: For a nonzero real # P, parabolas have the following equations & characteristics:

x2 = 4py y2 = 4px Focus at (0, P) Focus at (P, 0) Directrix: y = -p Directrix: x = -p Axis of symmetry: y-axis when vertex is on y-axis Equation x = 0 Axis of symmetry: x-axis when vertex is on x-axis Equation y = 0 If p > 0, then the parabola opens up. If p > 0, then the parabola opens right. If p < 0, then the parabola opens down. If p < 0, then the parabola opens left.

Ex. #1 Find the equation of the parabola with vertex (0, 0) that satisfies the given information: a. axis y = 0 b. focus (3.5, 0) passing through (2, 12)

Ex. #2 Find the focus & directrix. x = ½ y2 b. x = -6y2

Ex. #3 Find the equation of the parabola centered at the origin & passing through the given points. (3, - 3 2 ) & (3, 3 2 ) b. (-2, -5) & (2, -5)