document.write( "Question 83414: Use the definition of a parabola to show that the parabola with the vertex(h,k) and focus (h,k-c) has the equation $\"+%28x-h%29%5E2=-4c%28y-k%29\"$ . Show all work.
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Algebra.Com's Answer #59979 by scott8148(6628) $\"\"$ $\"About$

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a parabola is the locus of points that are equidistant from a given point (focus) and a given line (directrix)\r
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\n" ); document.write( "\n" ); document.write( "the vertex is located midway between the focus and the directrix, which means the equation for the directrix is y=k+c\r
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\n" ); document.write( "\n" ); document.write( "using the distance formula, the equation for a point (x,y) is (x-h)^2+(y-(k-c))^2=(y-(k+c))^2\r
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\n" ); document.write( "\n" ); document.write( "expanding gives (x-h)^2+y^2-2ky+2cy+k^2-2kc+c^2=y^2-2ky-2cy+k^2+2kc+c^2\r
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\n" ); document.write( "\n" ); document.write( "subtracting y^2-2ky+k^2+c^2 gives (x-h)^2+2cy-2kc=-2cy+2kc ... adding 2kc-2cy gives (x-h)^2=4kc-4cy\r
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\n" ); document.write( "\n" ); document.write( "factoring gives (x-h)^2=-4c(y-k) \n" ); document.write( "

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