document.write( "Question 193913: Write an equation of a parabola with a vertex at the origin.\r
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\n" ); document.write( "\n" ); document.write( "8. focus (0, 2)
\n" ); document.write( "9. focus (4, 0)
\n" ); document.write( "10. directrix at y = -8 \n" ); document.write( "
Algebra.Com's Answer #145729 by nerdybill(7384)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "8. focus (0, 2)
\n" ); document.write( "This is a \"vertical\" parabola, if so, it follows:
\n" ); document.write( "\"y+=+%281%2F%284c%29%29%28x-h%29%5E2+%2B+k\"
\n" ); document.write( ".
\n" ); document.write( "Since, the vertex is at the origin:
\n" ); document.write( "(h,k) = (0,0)
\n" ); document.write( "'c' is the distance from the vertex to the focus
\n" ); document.write( "therefore
\n" ); document.write( "c =2
\n" ); document.write( "Now, we plug it in to
\n" ); document.write( "\"y+=+%281%2F%284c%29%29%28x-h%29%5E2+%2B+k\"
\n" ); document.write( "\"y+=+%281%2F%284%2A2%29%29%28x-0%29%5E2+%2B+0\"
\n" ); document.write( "\"y+=+%281%2F8%29x%5E2\"
\n" ); document.write( ".
\n" ); document.write( "9. focus (4, 0)
\n" ); document.write( "This is a \"horizontal\" parabola, if so, it follows:
\n" ); document.write( "\"x+=+%281%2F%284c%29%29%28y-k%29%5E2+%2B+h\"
\n" ); document.write( ".
\n" ); document.write( "Since, the vertex is at the origin:
\n" ); document.write( "(h,k) = (0,0)
\n" ); document.write( "'c' is the distance from the vertex to the focus
\n" ); document.write( "therefore
\n" ); document.write( "c =4
\n" ); document.write( ".
\n" ); document.write( "Now, we plug it in to
\n" ); document.write( "\"x+=+%281%2F%284c%29%29%28y-k%29%5E2+%2B+h\"
\n" ); document.write( "\"x+=+%281%2F%284%2A4%29%29%28y-0%29%5E2+%2B+0\"
\n" ); document.write( "\"x+=+%281%2F16%29y%5E2\"
\n" ); document.write( ".
\n" ); document.write( "10. directrix at y = -8
\n" ); document.write( "This is a \"vertical\" parabola, if so, it follows:
\n" ); document.write( "\"y+=+%281%2F%284c%29%29%28x-h%29%5E2+%2B+k\"
\n" ); document.write( ".
\n" ); document.write( "Since, the vertex is at the origin:
\n" ); document.write( "(h,k) = (0,0)
\n" ); document.write( "'c' is the distance from the vertex to the directrix
\n" ); document.write( "therefore
\n" ); document.write( "c =-8
\n" ); document.write( "Now, we plug it in to
\n" ); document.write( "\"y+=+%281%2F%284c%29%29%28x-h%29%5E2+%2B+k\"
\n" ); document.write( "\"y+=+%281%2F%284%28-8%29%29%29%28x-0%29%5E2+%2B+0\"
\n" ); document.write( "\"y+=+%28-1%2F32%29x%5E2\"
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