document.write( "Question 1127410: find the centre,foci,vertices,and graph the following conics
\n" ); document.write( "1)8y²+12x=0
\n" ); document.write( "2)9x²-4y²-18x-16y-43=0
\n" ); document.write( "3)9x²+4y²-18x+16y-11=0
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Algebra.Com's Answer #743860 by MathLover1(20849)\"\" \"About 
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find the center,foci,vertices,and graph the following conics\r
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\n" ); document.write( "\"8y%5E2%2B12x=0\" -> Parabola with horizontal axis:\"%28y-k%29%5E2=4p%28x-h%29\"\r
\n" ); document.write( "\n" ); document.write( "Vertex is (\"h\",\"k\") \r
\n" ); document.write( "\n" ); document.write( "Focus is (\"h%2Bp\",\"k\") \r
\n" ); document.write( "\n" ); document.write( "Directrix is the line \"x=h-p\"\r
\n" ); document.write( "\n" ); document.write( "Axis is the line \"y=k\"\r
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\n" ); document.write( "\n" ); document.write( "\"8y%5E2=+-12x\"\r
\n" ); document.write( "\n" ); document.write( "\"y%5E2=-%2812%2F8%29x\"\r
\n" ); document.write( "\n" ); document.write( "\"y%5E2=-%283%2F2%29x\"...i you compare to \"%28y-k%29%5E2=4p%28x-h%29\", you see that\r
\n" ); document.write( "\n" ); document.write( "=> \"h=0\", \"k=0\" ->Vertex is (\"0\",\"0\")\r
\n" ); document.write( "\n" ); document.write( "Axis is the line \"y=0\"\r
\n" ); document.write( "\n" ); document.write( "\"4p=-%283%2F2%29\" -> \"p=-%283%2F%282%2A4%29%29\" -> \"p=-%283%2F8%29\" \r
\n" ); document.write( "\n" ); document.write( "Focus is (\"h%2Bp\",\"k\")->(\"0-3%2F8\",\"0\")->(\"-3%2F8\",\"0\")\r
\n" ); document.write( "\n" ); document.write( "Directrix is the line \"x=h-p\" ->\"x=0-%28-3%2F8%29\"->\"+x=3%2F8\"\r
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\n" ); document.write( "\n" ); document.write( "\"9x%5E2-4y%5E2-18x-16y-43=0\" ->hyperbola\r
\n" ); document.write( "\n" ); document.write( "\"9x%5E2-18x-4y%5E2-16y=43\"\r
\n" ); document.write( "\n" ); document.write( "\"%289x%5E2-18x%29-%284y%5E2%2B16y%29=43\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x%5E2-2x%29-4%28y%5E2%2B4y%29=43\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x%5E2-2x%2Bb%5E2%29+-9b%5E2+-4%28y%5E2%2B4y%2Bb%5E2%29+-4b%5E2=43\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x%5E2-2x%2Bb%5E2%29+-9b%5E2+-4%28y%5E2%2B4y%2Bb%5E2%29+-4b%5E2=43\"\r
\n" ); document.write( "\n" ); document.write( "since \"a=1\",\"2ab=2\"->\"b=1\"; for \"y\" part \"a=1\", \"2ab=4\"->\"b=2\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x-1%29%5E2+-9%2A1%5E2+-4%28y%2B2%29%5E2+-%28-4%29%2A2%5E2=43\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x-1%29%5E2+-9+-4%28y%2B2%29%5E2+%2B16=43\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x-1%29%5E2++-4%28y%2B2%29%5E2+%2B7=43\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x-1%29%5E2++-4%28y%2B2%29%5E2+=43-7\"\r
\n" ); document.write( "\n" ); document.write( "\"9+%28x+-+1%29%5E2+-+4+%28y+%2B+2%29%5E2++=+36\"\r
\n" ); document.write( "\n" ); document.write( "\"9+%28x+-+1%29%5E2+%2F36-+4+%28y+%2B+2%29%5E2%2F36++=+36%2F36\"\r
\n" ); document.write( "\n" ); document.write( " \"%28x+-+1%29%5E2+%2F4-++%28y+%2B+2%29%5E2%2F9++=+1\"\r
\n" ); document.write( "\n" ); document.write( "Center is (\"h\",\"k\") .\r
\n" ); document.write( "\n" ); document.write( "\"c%5E2=a%5E2%2Bb%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"h=1\"\r
\n" ); document.write( "\n" ); document.write( "\"k=-2\"\r
\n" ); document.write( "\n" ); document.write( "\"a=2\" ->semi-major axis length\r
\n" ); document.write( "\n" ); document.write( "\"b=3\"->semi-minor axis length\r
\n" ); document.write( "\n" ); document.write( "\"c=sqrt%282%5E2%2B3%5E2%29=sqrt%2813%29\"\r
\n" ); document.write( "\n" ); document.write( "center: (\"1\",\"-2\")\r
\n" ); document.write( "\n" ); document.write( "vertices: (\"-1\",\"+-2\") and (\"3\",\"+-2\")\r
\n" ); document.write( "\n" ); document.write( "foci: (\"1+-+sqrt%2813%29\", \"-2\") and (\"1+%2B+sqrt%2813%29\", \"-2\") ≈(\"-2.6\", \"-2\") and (\"4.6\", \"-2\")\r
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\n" ); document.write( "\n" ); document.write( "\"9x%5E2%2B4y%5E2-18x%2B16y-11=0\" ->ellipse\r
\n" ); document.write( "\n" ); document.write( "\"%289x%5E2-18x%29%2B%284y%5E2%2B16y%29=11\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x%5E2-2x%29%2B4%28y%5E2%2B4y%29=11\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x%5E2-2x%2B1%5E2%29+-9%2A1%5E2%2B4%28y%5E2%2B4y%2B2%5E2%29+-4%2A2%5E2=11\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x-1%29%5E2+-9%2B4%28y%2B2%29%5E2-16=11\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x-1%29%5E2+%2B4%28y%2B2%29%5E2-25=11\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x-1%29%5E2+%2B4%28y%2B2%29%5E2=11%2B25\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x-1%29%5E2+%2B4%28y%2B2%29%5E2=36\"\r
\n" ); document.write( "\n" ); document.write( "\"9%28x-1%29%5E2%2F36+%2B4%28y%2B2%29%5E2%2F36=36%2F36\"\r
\n" ); document.write( "\n" ); document.write( "\"%28x-1%29%5E2%2F4+%2B%28y%2B2%29%5E2%2F9=1\"->Ellipse with vertical major axis:\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"\r
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\n" ); document.write( "\n" ); document.write( "\"h=1\"\r
\n" ); document.write( "\n" ); document.write( "\"k=-2\"\r
\n" ); document.write( "\n" ); document.write( "\"a=3\" ->semi-major axis length\r
\n" ); document.write( "\n" ); document.write( "\"b=2\"->semi-minor axis length\r
\n" ); document.write( "\n" ); document.write( "\"c=sqrt%282%5E2%2B3%5E2%29=sqrt%2813%29\"\r
\n" ); document.write( "\n" ); document.write( "center: (\"1\",\"-2\")
\n" ); document.write( "foci : (\"1\", \"-2+-+sqrt%285%29\") and (\"1\", \"-2+%2B+sqrt%285%29\")≈(\"1\", \"-4.2\") and (\"1\",\"+0.2\")\r
\n" ); document.write( "\n" ); document.write( "vertices: (\"1\",\"+-5\") and (\"1\", \"1\")\r
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