document.write( "Question 196705: I cannot seem to find the correct standard equation, foci, and asymptotes of the following hyperbola:
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\n" ); document.write( "\n" ); document.write( "I need to write it in this kind of form:
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\n" ); document.write( "\n" ); document.write( "I have been solving these kinds of problems wrong lately, and I am quite worried since it will be a subject on an upcoming test. Any help would be appreciated, and many thanks in advance. \n" ); document.write( "

Algebra.Com's Answer #147433 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
I cannot seem to find the correct standard equation, foci, and asymptotes of the following hyperbola:\r
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document.write( "Rearrange so that the two terms in x are next to\r\n" );
document.write( "each other and the two terms in y are next to\r\n" );
document.write( "each other, and 11 to both sides:\r\n" );
document.write( "sides:\r\n" );
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document.write( "The coefficient of  is already 1, so\r\n" );
document.write( "we don't factor anything out of it, just enclose the\r\n" );
document.write( "first two terms in parentheses:\r\n" );
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document.write( "Now factor only -4 (not y) out of the last two terms\r\n" );
document.write( "on the left.\r\n" );
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document.write( "Complete the square in each parentheses.  \r\n" );
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document.write( "In the first parentheses multiply the  coefficient of\r\n" );
document.write( "x by , getting .  Then we square ,\r\n" );
document.write( "getting .  So we add 9 to both sides:\r\n" );
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document.write( "Now we factor the first parentheses as \r\n" );
document.write( "or \r\n" );
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document.write( "In the second parentheses multiply the  coefficient of\r\n" );
document.write( "y by , getting .  Then we square ,\r\n" );
document.write( "getting .  So we add 4 inside the second\r\n" );
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document.write( "But since there is a  factor in front of the second\r\n" );
document.write( "parentheses, when we add  inside the second parentheses\r\n" );
document.write( "we are really adding  times  or  to the\r\n" );
document.write( "left side, so we must add  to the right side too.\r\n" );
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document.write( "Now we factor the second parentheses as \r\n" );
document.write( "or \r\n" );
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document.write( "Next we get a  on the right side by dividing\r\n" );
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document.write( "Now to get rid of the 4 on top on the second term, we\r\n" );
document.write( "divide top and bottom by 4\r\n" );
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document.write( "Can you go from here? \r\n" );
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document.write( "Compare to\r\n" );
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document.write( "So , , , \r\n" );
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document.write( "So center = (h,k) = (3,-2)\r\n" );
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document.write( "The two vertices are a=2 units left and right of the\r\n" );
document.write( "center, so they are (1,-2) and (5,-2)\r\n" );
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document.write( "The two foci are  units left and right of the center.\r\n" );
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document.write( "First we calculate  using\r\n" );
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document.write( "So the two foci are  units left and right of the\r\n" );
document.write( "center, so they are (,-2) and (,-2)\r\n" );
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document.write( "The asymptotes have slopes which are ą or\r\n" );
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document.write( "And the go through the center (3,-2), so we use the\r\n" );
document.write( "point slope formula:\r\n" );
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document.write( "For the asymptote that has slope :\r\n" );
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document.write( "Multiply both sides by 2\r\n" );
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document.write( "---------------\r\n" );
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document.write( "For the asymptote that has slope :\r\n" );
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document.write( "Multiply both sides by -2\r\n" );
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document.write( "Edwin

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