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Writing and Graphing Parabolas Every parabola has the property that any point on it is equidistant from a point called the focus (which lies on the axis of symmetry) and a line called the directrix ( which is perpendicular to the axis of symmetry). Standard Equation of a Parabola (Vertex at Origin) The standard form of the equation of a parabola with vertex (0,0) is as follows. Equation Focus Directrix x2 = 4py y2=4px (0, p) (p,0) y= -p x= -p Graphing an equation of a Parabola Graph the parabola- label the focus and directrix x2=16y Axis of Symmetry Vertical (x=0) Horizontal (y=0) y2 = -8x Writing the Equation of a parabola 1. Write an equation of the parabola with vertex (0,0) and focus( 4,0) 2. Write an equation of a parabola with vertex (0,0) and focus (0, ¼) One of the largest radio telescopes has a diameter of 250 feet and a focal length of 50 feet. If the cross section of the radio telescope is a parabola, find the depth.