document.write( "Question 544860: What is the equation for a parabola in which the set of all points in the plane are equidistant from the focus and line. F(0, -5); y=5 \n" ); document.write( "

Algebra.Com's Answer #355314 by lwsshak3(11628) $\"\"$ $\"About$

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What is the equation for a parabola in which the set of all points in the plane are equidistant from the focus and line. F(0, -5); y=5
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\n" ); document.write( "What you have here is the definition of a parabola.
\n" ); document.write( "Axis of symmetry: x=0 or y-axis
\n" ); document.write( "Since y-coordinate of focus(-5) is below the directrix(y=5), parabola opens downward.
\n" ); document.write( "Standard form of equation for this parabola: (x-h)^2=-4p(y-k), with (h,k)=(x,y) coordinates of the vertex.
\n" ); document.write( "x-coordinate of vertex=x-coordinate of focus=0
\n" ); document.write( "y-coordinate of vertex=midway between y-coordinate of focus and directrix on the axis of symmetry=0
\n" ); document.write( "vertex: (0,0)
\n" ); document.write( "p=distance from vertex to focus or directrix on the axis of symmetry=5
\n" ); document.write( "4p=20
\n" ); document.write( "Equation of given parabola:
\n" ); document.write( "(x-h)^2=-4p(y-k)
\n" ); document.write( "(x-0)^2=-20(y-0)
\n" ); document.write( "x^2=-20y \n" ); document.write( "

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