document.write( "Question 470747: 9x^2 – 25y^2 + 150y – 450 = 0
\n" ); document.write( "Find the center, vertices, foci, and asymptotes of the hyperbola \n" ); document.write( "
Algebra.Com's Answer #323131 by lwsshak3(11628)\"\" \"About 
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9x^2 – 25y^2 + 150y – 450 = 0
\n" ); document.write( "Find the center, vertices, foci, and asymptotes of the hyperbola
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\n" ); document.write( "9x^2 – 25y^2 + 150y – 450 = 0
\n" ); document.write( "9x^2 – 25y^2 + 150y = 450
\n" ); document.write( "9x^2-25(y^2+6y+9)=450-225=225
\n" ); document.write( "9x^2-25(y+9)^2=225
\n" ); document.write( "x^2/25-(y+9)^2/9=1
\n" ); document.write( "This is a hyperbola with horizontal transverse axis, opens sideways.
\n" ); document.write( "Standard form: (x-h)^2/a^2-(y-k)^2/b^2=1
\n" ); document.write( "Center: (0,-9)
\n" ); document.write( "a^2=25
\n" ); document.write( "a=5
\n" ); document.write( "length of transverse axis=2a=10
\n" ); document.write( "vertices: (0±5,-9)
\n" ); document.write( "..
\n" ); document.write( "b^2=9
\n" ); document.write( "b=3
\n" ); document.write( "length of conjugate axis=2b=6
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2+b^2=25+9=34
\n" ); document.write( "c=√34
\n" ); document.write( "Foci: (0±√34,-9)
\n" ); document.write( "..
\n" ); document.write( "Asymptotes:
\n" ); document.write( "slope, m=±b/a=±3/5
\n" ); document.write( "y= ±mx+b
\n" ); document.write( "b=y-intercept=-9 (at center)
\n" ); document.write( "Equation of asymptotes:
\n" ); document.write( "y=±3x/5-9\r
\n" ); document.write( "\n" ); document.write( "see graph below as a visual check on answers.\r
\n" ); document.write( "\n" ); document.write( "..
\n" ); document.write( "y=±(9x^2/25-9)^.5-9
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