document.write( "Question 1142038: Determine which of the conic sections is represented.\r
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Algebra.Com's Answer #762789 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Your conic section is presented by equation\r\n" );
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document.write( "    4x² + 14xy + 5y² + 18x − 6y + 30 = 0.\r\n" );
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document.write( "The equation has a mixed term xy -- therefore, it may happen that the standard high school knowledge is not enough \r\n" );
document.write( "to answer the question.\r\n" );
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document.write( "But the answer does exist in Analytic Geometry.\r\n" );
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document.write( "To determine the type of the conic section, calculate the discriminant \r\n" );
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document.write( "    d = B^2 - 4*A*C,\r\n" );
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document.write( "where  B = 14 is the coefficient at the \"xy\"-term;\r\n" );
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document.write( "       A = 4  is the coefficient at the \"x^2\"-term;\r\n" );
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document.write( "       C = 5  is the coefficient at the \"y^2\"-term.\r\n" );
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document.write( "In your case  the discriminant  d =  =  116  is a positive real number.\r\n" );
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document.write( "It means that the conic section is a HYPERBOLA.\r\n" );
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document.write( "For details, read your textbook or learn from the universal source WIKIPEDIA - see Wikipedia article  \r\n" );
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document.write( "    https://en.wikipedia.org/wiki/Conic_section\r\n" );
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document.write( "    https://en.wikipedia.org/wiki/Conic_section\r\n" );
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