document.write( "Question 820619: how do i find the asymptotes for (y^2/16)-(x^2/81)=1 \n" ); document.write( "
Algebra.Com's Answer #493639 by lwsshak3(11628)\"\" \"About 
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how do i find the asymptotes for
\n" ); document.write( "(y^2/16)-(x^2/81)=1
\n" ); document.write( "This is an equation of a hyperbola with vertical transverse axis.
\n" ); document.write( "Its standard form of equation: \"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\", (h,k)=(x,y) coordinates of center.
\n" ); document.write( "..
\n" ); document.write( "Asymptotes of hyperbolas are straight-line equations that go through the center.
\n" ); document.write( "Their standard form: y=mx+b, m=slope, b=y-intercept
\n" ); document.write( "slopes of hyperbolas with vertical transverse axis=±a/b
\n" ); document.write( "slopes of hyperbolas with horizontal transverse axis=±b/a
\n" ); document.write( "..
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "center: (0,0)
\n" ); document.write( "a^2=16
\n" ); document.write( "a=√16=4
\n" ); document.write( "b^2=81
\n" ); document.write( "b=√81=9
\n" ); document.write( "slopes of asymptotes=±a/b=±4/9
\n" ); document.write( "..
\n" ); document.write( "Equation of asymptote with positive slope:
\n" ); document.write( "y=(4/9)x+b
\n" ); document.write( "solve for b using coordinates of center:
\n" ); document.write( "b=y-intercept=0
\n" ); document.write( "equation: y=4x/9
\n" ); document.write( "..
\n" ); document.write( "Equation of asymptote with negative slope:
\n" ); document.write( "y=(-4/9)x+b
\n" ); document.write( "b=0
\n" ); document.write( "equation:y=-4x/9 \n" ); document.write( "
\n" );