MA 154 Lesson 25 DelworthMA 154 Lesson 25 DelworthSection 11.1 ParabolasA parabola is the set of all points in a plane equidistant from a fixed point F (the focus) and a fixed line l (the directrix) that lie in the plane.The axis of the parabola is the line through F that is perpendicular to the directrix.The vertex of the parabola is the point V on the axis halfway from F to l. The vertex is the point on the parabola that is closest to the directrix.The vertex and focus are points; the directrix and axis are lines.The distance from the vertex to the focus and from the vertex to the directrix is p units.The distance from the focus to the directrix is 2p units.If the parabola has a vertical axis and its vertex is at (0, 0), its formula is: x24 pyIf the parabola has a horizontal axis and its vertex is at (0, 0), its formula is: y24 pxThe proof of this is not too bad. I will do it for a vertical parabola:Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix.x28y2y2 5x1MA 154 Lesson 25 DelworthSection 11.1 ParabolasIf we take the standard equation of a parabola and replace x with x – h and y with y – k, then x24 pybecomes x h 24 p y k and y24 px becomes y k 24 p x h with vertex V(h, k).Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix.y 2 212(x 1)x 3 213y 2 y214y 4x 45 0x2 20y 10Sketch the parabola described and find an equation for the parabola.V(3, –1), F(3, 2) V(–2, 3), F(–6,
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