9.4, 9.5 - Conics - Sections 9.4 and 9.5 - Conics and...

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Sections 9.4 and 9.5 - Conics and Calculus Parabolas —A parabola is the set of all points ( x, y ) in the plane that are equidistant from a fixed line (directrix) and a fixed point (focus). The Standard Form of the equation of a parabola with vertex ( h, k ) and directrix p k y is ) ( 4 ) ( 2 k y p h x For this type, the axis is vertical (i.e. the parabola opens up or down) For a directrix p h x , the equation is ) ( 4 ) ( 2 h x p k y . Here the axis is horizontal, or the parabola opens to the side Note: For parabolas , the vertex is always p units from both the focus and the directrix . If you know two pieces of information from among vertex, focus, directrix, p, you can find everything there is to know about a parabola. Also note that general form for a parabola is c bx ax y 2 (opens up or down) or c by ay x 2 (opens sideways). When given in this form p a 4 1 and you can find the vertex using either College Algebra or Calc I techniques For each of the examples below, find the vertex, focus, and directrix of the parabola, and sketch the graph.
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9.4, 9.5 - Conics - Sections 9.4 and 9.5 - Conics and...

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