8.1 Parabola comp.notebook April 22, 2014 8.1 Conics Conic sections are cross sections of a cone. The three basic conics are: 1) Parabola 2) Ellipse 3) Hyperbola The general conic equation is a quadratic in two variables: Ax2 + Bxy + Cy2 + Dx + Ey + F=0 8.1 Parabola comp.notebook April 22, 2014 Parabola A parabola is the set of all points in a plane equidistant from a line the directrix and a point – the focus. 8.1 Parabola comp.notebook April 22, 2014 Parabola Standard Eqn: x2=4py Opens: Focus Directrix Axis Focal length Focal width Up or down (0,p) y=p yaxis p |4p| or y2=4px Right or left (p,0) x=p xaxis p |4p| 8.1 Parabola comp.notebook Ex. 1 Find the focus, directrix and focal width of the parabola y = 4x2 April 22, 2014 8.1 Parabola comp.notebook April 22, 2014 Ex. 2 Find an equation in standard form for the parabola whose directrix is the line x=3 and whose focus is the point (3,0). 8.1 Parabola comp.notebook April 22, 2014 Parabola vertex (h,k) or (yk)2=4p(xh) Standard Eqn: (xh)2=4p(yk) Opens: Focus Directrix Axis Focal length Focal width Up or down (h,k+p) y=kp x=h p |4p| Right or left (h+p,k) x=hp y=k p |4p| 8.1 Parabola comp.notebook Ex. 3 Find the standard form of the parabola with vertex (5,5) and focus (3,5). April 22, 2014 8.1 Parabola comp.notebook Ex. 4 Prove that the graph of y2 4x + 6y +29=0 is a parabola, find its vertex, focus and directrix and sketch the parabola. Confirm this on your grapher. Ex. 5 Find the equation of the parabola with focus (4, 6) and directrix x=1. April 22, 2014 8.1 Parabola comp.notebook April 22, 2014 Ex. 6 The reflector of a television satellite dish is a paraboloid of revolution with diameter 5ft and a depth of 2ft. How far from the vertex should the antenna be placed?
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