document.write( "Question 681942: Find the equation of a hyberbola with transverse axis on the line y= -5, length of transverse axis = 6, conjugate axis on the line x=2. and length of conjugate axis=6. Expres the answer in the form Ax^2 + Cy^2 + Dx + Ey + F = 0. \n" ); document.write( "

Algebra.Com's Answer #422869 by Edwin McCravy(20060) $\"\"$ $\"About$

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Find the equation of a hyberbola with transverse axis on the line y= -5, length of transverse axis = 6, conjugate axis on the line x=2. and length of conjugate axis=6. Expres the answer in the form Ax^2 + Cy^2 + Dx + Ey + F = 0.
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document.write( "The equation of such a hyperbola, with the transverse axis horizontal, is\r\n" );
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document.write( "where (h,k) is the center, a =  the length of the transverse axis,\r\n" );
document.write( "and b =  the length of the conjugate axis.\r\n" );
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document.write( "We'll begin by drawing the horizontal line y = -5 and the vertical line x = 2.\r\n" );
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document.write( "The transverse axis and the conjugate axis intersect at the center of the\r\n" );
document.write( "hyperbola which is (2,-5).  Now we'll leave just the transverse axis and the\r\n" );
document.write( "conjugate axis, which are given as 6 units each, and we'll and erase the rest\r\n" );
document.write( "of those green lines:\r\n" );
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document.write( "and draw the defining rectangle:\r\n" );
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document.write( "Now we can sketch in the asymptotes and the hyperbola:\r\n" );
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document.write( "We can write the equation of the hyperbola,\r\n" );
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document.write( "where (h,k) is the center (2,-5), a =  the length of the transverse\r\n" );
document.write( "axis =  = 3\r\n" );
document.write( "and b =  the length of the conjugate axis, also = 3\r\n" );
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document.write( "That is the equation in STANDARD, but the problem asks for it in the \r\n" );
document.write( "GENERAL form Ax² + Cy² + Dx + Ey + F = 0, so\r\n" );
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document.write( "Clear of fractions by multiplying through by 5\r\n" );
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document.write( "(x - 2)² - (y + 5)² = 9\r\n" );
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document.write( "x² - 4x + 4 - (y² + 10y + 25) = 9\r\n" );
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document.write( "x² - 4x + 4 - y² - 10y - 25 = 9\r\n" );
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document.write( "    x² - 4x - 21 - y² - 10y = 9\r\n" );
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document.write( "    x² - 4x - 30 - y² - 10y = 0\r\n" );
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document.write( "Rearrange the terms in the form Ax² + Cy² + Dx + Ey + F = 0\r\n" );
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document.write( "    x² - y² - 4x - 10y - 30 = 0\r\n" );
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document.write( "Edwin

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