document.write( "Question 878034: Find the vertices, foci, and equations of the asymptotes of the hyperbola. 4x^2-3y^2+8x+16=0 \n" ); document.write( "
Algebra.Com's Answer #529956 by lwsshak3(11628)\"\" \"About 
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Find the vertices, foci, and equations of the asymptotes of the hyperbola.
\n" ); document.write( "4x^2-3y^2+8x+16=0
\n" ); document.write( "4x^2+8x-3y^2=-16
\n" ); document.write( "complete the square
\n" ); document.write( "4(x^2+2x+1)-3y^2=-16+4
\n" ); document.write( "4(x+1)^2-3y^2=-12
\n" ); document.write( "divide by -12
\n" ); document.write( ", (h,k)=coordinates of center.
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "center: (-1,0)
\n" ); document.write( "a^2=4
\n" ); document.write( "a=2
\n" ); document.write( "vertices: (-1,0±a)=(-1,0±2)=(-1,-2) and (-1,2)
\n" ); document.write( "b^2=3
\n" ); document.write( "b=√3
\n" ); document.write( "c^2=a^2+b^2=4+3=7
\n" ); document.write( "c=√7≈2.7
\n" ); document.write( "foci: (-1,0±c)=(-1,0±2.7)=(-1,-2.7) and (-1,2.7)
\n" ); document.write( "...
\n" ); document.write( "Asymptotes are two straight line equations that go thru the center and are of the form: y=mx+b, m=slope, b=y-intercept.
\n" ); document.write( "slopes of asymptotes of hyperbolas with vertical transverse axis=±a/b=±2/√3
\n" ); document.write( "..
\n" ); document.write( "Equation of asymptote with negative slope, -2/√3:
\n" ); document.write( "y=-2x/√3+b
\n" ); document.write( "solving for b using coordinates of center(-1,0)
\n" ); document.write( "0=-2*-1/√3+b
\n" ); document.write( "b=-2/√3
\n" ); document.write( "equation: y=-2x/√3-2/√3
\n" ); document.write( "..
\n" ); document.write( "Equation of asymptote with positive slope, 2/√3:
\n" ); document.write( "y=2x/√3+b
\n" ); document.write( "solving for b using coordinates of center(-1,0)
\n" ); document.write( "0=2*-1/√3+b
\n" ); document.write( "b=2/√3
\n" ); document.write( "equation: y=2x/√3+2/√3 \n" ); document.write( "
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