document.write( "Question 87147: $\"%28x%2B2%29%5E2%2F9\"$ - $\"%28y-3%29%5E2%2F25\"$ = 1
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Algebra.Com's Answer #63337 by Edwin McCravy(20060) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( " -  = 1\r\n" );
document.write( "multi choice\r\n" );
document.write( "a. (-2,-2)and (-2,8)\r\n" );
document.write( "b. (-5,3)and (1,3)\r\n" );
document.write( "c. (5,-3)and (-1,-3)\r\n" );
document.write( "d. (2,2)and (2,-8)\r\n" );
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document.write( "You forgot to tell us what you are looking for!!!!!\r\n" );
document.write( "I'm guessing you want the vertices.  If so then\r\n" );
document.write( "\"b.\" is the correct choice, as you'll see below:\r\n" );
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document.write( "You'll have to learn all these things about\r\n" );
document.write( "x-hyperbolas (ones that open right and left, so I'll \r\n" );
document.write( "take this opportunity to explain all the parts of \r\n" );
document.write( "x-hyperbolas.\r\n" );
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document.write( "(Note: y-hyperbolas (ones that open upward and downward,\r\n" );
document.write( "are similar, except the y's and x's are reversed \r\n" );
document.write( "throughout. If you need to know about them please \r\n" );
document.write( "repost).\r\n" );
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document.write( " -  = 1\r\n" );
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document.write( "is the equation of a hyperbola (two branches)\r\n" );
document.write( "which opens right and left\r\n" );
document.write( "which has center (h,k)\r\n" );
document.write( "which has transverse axis = 2a\r\n" );
document.write( "which has semi-transverse axis = a\r\n" );
document.write( "which has which has vertices at the ends of the \r\n" );
document.write( "      transverse axis (h-a,k) and (h+a,k)\r\n" );
document.write( "which has conjugate axis = 2b\r\n" );
document.write( "which has semi-conjugate axis = b\r\n" );
document.write( "which has ends of conjugate axis (h,k+b) and (h,k-b)\r\n" );
document.write( "which has foci (h-c,k) and (h+c,k) where \r\n" );
document.write( "which has defining rectangle whose four corner points are\r\n" );
document.write( "          (h-a,k-b), (h-a,k+b), (h+a,k-b) and (h+a,k+b)\r\n" );
document.write( "which has asymptotes whose equations are \r\n" );
document.write( " and \r\n" );
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document.write( "So your problem is\r\n" );
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document.write( " -  = 1  \r\n" );
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document.write( "compare that with  \r\n" );
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document.write( " -  = 1\r\n" );
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document.write( "and we see that h=-2, a=3, k=3, b=5\r\n" );
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document.write( "So your equation is the equation of a hyperbola (two branches)\r\n" );
document.write( "which opens right and left\r\n" );
document.write( "which has center (-2,3)\r\n" );
document.write( "which has transverse axis = 2(3) = 6\r\n" );
document.write( "which has semi-transverse axis = 3\r\n" );
document.write( "which has which has vertices at the ends of the \r\n" );
document.write( "      transverse axis (-2-3,3) and (-2+3,3) or\r\n" );
document.write( "      (-5,3) and (1,3) [That's all you were asked for!]            \r\n" );
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document.write( "which has conjugate axis = 2(5) = 10\r\n" );
document.write( "which has semi-conjugate axis = 5\r\n" );
document.write( "which has ends of conjugate axis (-2,3+5) and (-2,3-5)\r\n" );
document.write( "      or (-2,8) and (-2,-2)\r\n" );
document.write( "which has vertices (-2-3,3) and (-2+3,3) or (-5,3) and (1,3)\r\n" );
document.write( "which has foci (-2-c,3) and (-2+c,3) where \r\n" );
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document.write( "So  = , and the foci are\r\n" );
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document.write( "(-2-,3) and (-2+,3)\r\n" );
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document.write( "which has defining rectangle whose four corner points are\r\n" );
document.write( "          (-2-3,3-5), (-2-3,3+5), (-2+3,3-5) and (-2+3,3+5)\r\n" );
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document.write( "or\r\n" );
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document.write( "(-5,-2), (-5,8), (1,-2), and (1,8)\r\n" );
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document.write( "which has asymptotes whose equations are \r\n" );
document.write( " and \r\n" );
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document.write( "or\r\n" );
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document.write( " and \r\n" );
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document.write( " and \r\n" );
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document.write( " and \r\n" );
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document.write( " and \r\n" );
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document.write( " and \r\n" );
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document.write( "To get the graph, we plot the center, then the \r\n" );
document.write( "transverse axis (which goes from vertex to vertex,\r\n" );
document.write( "and the ends of the conjugate axes\r\n" );
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document.write( "Next we draw the defining rectangle:\r\n" );
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document.write( "Next we draw AND EXTEND the diagonals of\r\n" );
document.write( "the defining rectangle, which are the\r\n" );
document.write( "asymptotes:\r\n" );
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document.write( "Then finally we sketch in the hyperbola to\r\n" );
document.write( "approach the asymptotes, and to just touch the\r\n" );
document.write( "defining rectangle at the vertices (ends of\r\n" );
document.write( "the transverse axes):\r\n" );
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document.write( "Edwin
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