document.write( "Question 422433: Choose the equation that best represents a hyperbola with vertices (0, –1) and (4, –1), and foci (–1, –1) and (5, –1).\r
\n" ); document.write( "\n" ); document.write( "(a) (x-2)^2/4 - (y+1)^2/5 = 1
\n" ); document.write( "(b) (x-2)^2/25 - (y+1)^2/16 =1
\n" ); document.write( "(c) (x+2)^2/4 + (y+1)^2/5 = 1
\n" ); document.write( "(d) x^2/4 - y^2/5 = 1 \n" ); document.write( "

Algebra.Com's Answer #294865 by Edwin McCravy(20056) $\"\"$ $\"About$

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(a) (x-2)^2/4 - (y+1)^2/5 = 1
\n" ); document.write( "(b) (x-2)^2/25 - (y+1)^2/16 =1
\n" ); document.write( "(c) (x+2)^2/4 + (y+1)^2/5 = 1
\n" ); document.write( "(d) x^2/4 - y^2/5 = 1
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document.write( "We can eliminate (c) immediately because the + sign makes it the\r\n" );
document.write( "equation of an ellipse, not a hyperbola.\r\n" );
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document.write( "The vertices are points on the curve, so we substitute the vertices\r\n" );
document.write( "(0, –1) and (4, –1) to see if (a) could be the correct answer:\r\n" );
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document.write( " (x-2)^2/4 - (y+1)^2/5 = 1\r\n" );
document.write( "(0-2)^2/4 - (-1+1)^2/5 = 1\r\n" );
document.write( "               4/4 - 0 = 1\r\n" );
document.write( "                     1 = 1\r\n" );
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document.write( " (x-2)^2/4 - (y+1)^2/5 = 1\r\n" );
document.write( "(4-2)^2/4 - (-1+1)^2/5 = 1\r\n" );
document.write( "               4/4 - 0 = 1\r\n" );
document.write( "                     1 = 1\r\n" );
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document.write( "So (a) could be the answer, but we aren't sure.\r\n" );
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document.write( "so we substitute the vertices\r\n" );
document.write( "(0, –1) and (4, –1) to see if (b) could be the correct answer:\r\n" );
document.write( "\r\n" );
document.write( " (x-2)^2/25 - (y+1)^2/16 = 1\r\n" );
document.write( "(0-2)^2/25 - (-1+1)^2/16 = 1\r\n" );
document.write( "                4/25 - 0 = 1\r\n" );
document.write( "                    4/25 = 1\r\n" );
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document.write( "So we have ruled out (b) without even bothering to substitute\r\n" );
document.write( "the other vertex.\r\n" );
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document.write( "The only other choice is (d), so we substitute the vertices\r\n" );
document.write( "(0, –1) and (4, –1) to see if (d) could be the correct answer:\r\n" );
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document.write( "           x^2/4 - y^2/5 = 1\r\n" );
document.write( "          0^2/4 - (-1)/5 = 1 \r\n" );
document.write( "                 0 + 1/5 = 1\r\n" );
document.write( "                     1/5 = 1\r\n" );
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document.write( "So we have ruled out (d) without even bothering to substitute\r\n" );
document.write( "the other vertex.\r\n" );
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document.write( "So the only possible answer is (a).\r\n" );
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document.write( "Edwin

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