document.write( "Question 734909: Find an asymptote of this conic section..
\n" ); document.write( "9x^2-36x-4y^2+24y-36=0 \n" ); document.write( "

Algebra.Com's Answer #449456 by lwsshak3(11628) $\"\"$ $\"About$

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Find an asymptote of this conic section..
\n" ); document.write( "9x^2-36x-4y^2+24y-36=0
\n" ); document.write( "complete the square:
\n" ); document.write( "9(x^2-4x+4)-4(y^2-6y+9)=36+36-36
\n" ); document.write( "9(x-2)^2-4(y-3)^2=36
\n" ); document.write( " $\"%28x-2%29%5E2%2F4-%28y-3%29%5E2%2F9=1\"$
\n" ); document.write( "This is an equation of a hyperbola with horizontal transverse axis:
\n" ); document.write( "Its standard form of equation: $\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"$ , (h,k)=(x,y) coordinates of center
\n" ); document.write( "For given equation:
\n" ); document.write( "center: (2,3)
\n" ); document.write( "a^2=4
\n" ); document.write( "a=2
\n" ); document.write( "b^2=9
\n" ); document.write( "b=3
\n" ); document.write( "Slopes of asymptotes for hyperbolas with horizontal transverse axis=ąb/a=ą3/2
\n" ); document.write( "Asymptotes are equations of straight lines that go thru the center of the hyperbola: y=mx+b, m=slope, b=y-intercept
\n" ); document.write( "..
\n" ); document.write( "Equation of asymptote with negative slope, m=-3/2
\n" ); document.write( "y=-3x/2+b
\n" ); document.write( "solve for b using coordinates of the center (2,3)
\n" ); document.write( "3=-3*2/2+b
\n" ); document.write( "b=6
\n" ); document.write( "equation:y=-3x/2+6
\n" ); document.write( "..
\n" ); document.write( "Equation of asymptote with positive slope, m=3/2
\n" ); document.write( "y=3x/2+b
\n" ); document.write( "solve for b using coordinates of the center (2,3)
\n" ); document.write( "3=3*2/2+b
\n" ); document.write( "b=0
\n" ); document.write( "equation:y=3x/2
\n" ); document.write( "..
\n" ); document.write( "Equations of asymptotes: y=-3x/2+6 and y=3x/2 \n" ); document.write( "

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