document.write( "Question 1087980: Find the standard form of the equation of the hyperbola with vertices at (2,0) and (6,0) and foci at (0,0) and (8,0). \n" ); document.write( "

Algebra.Com's Answer #702263 by ikleyn(53765) $\"\"$ $\"About$

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document.write( "The length of the real axis of the hyperbola is 6 - 2 = 4,\r\n" );
document.write( "and the real axis is the horizontal line y = 0 coinciding with x-axis.\r\n" );
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document.write( "The real semi-axis length is a =  = 2.\r\n" );
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document.write( "The center of the hyperbola is the midpoint between (0,0) and (8,0).\r\n" );
document.write( "So, the center is the point (4,0).\r\n" );
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document.write( "The foci distance is 8 - 0 = 8.\r\n" );
document.write( "The half of the foci distance is  = 4.\r\n" );
document.write( "It is the distance from the hyperbola center to the focus point, which is traditionally called \"c\".\r\n" );
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document.write( "The imaginary semi-axis \"b\" is   =  =  = 12.\r\n" );
document.write( "Hence, b = .\r\n" );
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document.write( "Thus the hyperbola standard form equation is\r\n" );
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document.write( " -  = 1,\r\n" );
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document.write( "or, which is the same,  \r\n" );
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document.write( " -  = 1.\r\n" );
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document.write( "Hyperbola  -  = 1  \r\n" );
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document.write( "The foci are (0,0) and (8,0).\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Hyperbola definition, canonical equation, characteristic points and elements \r
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\n" ); document.write( "\n" ); document.write( "    - Standard equation of a hyperbola \r
\n" ); document.write( "\n" ); document.write( "    - Identify elements of hyperbola given by its standard equation \r
\n" ); document.write( "\n" ); document.write( "    - Find the standard equation of a hyperbola given by its elements \r
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\n" ); document.write( "\n" ); document.write( "    - General equation of a hyperbola\r
\n" ); document.write( "\n" ); document.write( "    - Transform general equation of a hyperbola to the standard form by completing the square \r
\n" ); document.write( "\n" ); document.write( "    - Identify elements of a hyperbola given by its general equation \r
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\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on hyperbolas \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Conic sections: Hyperbolas. Definition, major elements and properties. Solved problems\".\r
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