document.write( "Question 1121260: Find the Standard equation of hyperbola, center, foci, vertices at asymptotes of the function 4x²-5y²+32x+30y=1.
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Algebra.Com's Answer #737091 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "Find the Standard equation of hyperbola, center, foci, vertices at asymptotes of the function 4x² - 5y² + 32x + 30y = 1.
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document.write( "4x^2 - 5y^2 + 32x + 30y = 1  ====>  Complete the squares for x- and y-terms separately  ====>  \r\n" );
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document.write( "(4x^2 + 32x) + (-5y^2 + 30y) = 1\r\n" );
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document.write( "4(x^2 + 8x) - 5*(y^2 - 6y) = 1\r\n" );
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document.write( "4*(x^2 + 8x + 16) - 5*(y^2 - 6y + 9) = 1 + 4*16 - 5*9\r\n" );
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document.write( "4*(x+4)^2 - 5*(y-3)^2 = 20.     <<<---=== Divide by 20 both sides\r\n" );
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document.write( " -  = 1\r\n" );
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document.write( " -  = 1\r\n" );
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document.write( "It is the standard form equation for a hyperbola.\r\n" );
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document.write( "The hyperbola has the center at  (x,y) = (-4,3).\r\n" );
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document.write( "Real axis is parallel to x-axis; imaginary axis is parallel to y-axis.\r\n" );
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document.write( "Real semi-axis is  units long;  Imaginary axis is 2 units long.\r\n" );
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document.write( "Vertices are at y= 3:  x =   and  x= .\r\n" );
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document.write( "The foci are  x=  = -4 - 3 = -7  and  x=  = -4 + 3 = -1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Hyperbola definition, canonical equation, characteristic points and elements \r
\n" ); document.write( "\n" ); document.write( "    - Hyperbola focal property \r
\n" ); document.write( "\n" ); document.write( "    - Tangent lines and normal vectors to a hyperbola \r
\n" ); document.write( "\n" ); document.write( "    - Optical property of a hyperbola \r
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\n" ); document.write( "\n" ); document.write( "    - Standard equation of a hyperbola \r
\n" ); document.write( "\n" ); document.write( "    - Identify elements of hyperbola given by its standard equation \r
\n" ); document.write( "\n" ); document.write( "    - Find the standard equation of a hyperbola given by its elements \r
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\n" ); document.write( "\n" ); document.write( "    - General equation of a hyperbola\r
\n" ); document.write( "\n" ); document.write( "    - Transform general equation of a hyperbola to the standard form by completing the square \r
\n" ); document.write( "\n" ); document.write( "    - Identify elements of a hyperbola given by its general equation \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Conic sections: Hyperbolas. Definition, major elements and properties. Solved problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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