document.write( "Question 613530: the question says find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola (x+1)sqared -(y-3)sqared=4
\n" ); document.write( "please help im so lost \n" ); document.write( "
Algebra.Com's Answer #386086 by lwsshak3(11628)\"\" \"About 
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the question says find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola (x+1)sqared -(y-3)sqared=4
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\n" ); document.write( "(x+1)^2-(y-3)^2=4
\n" ); document.write( "(x+1)^2/4-(y-3)^2/4=1This is an equation of a hyperbola with horizontal transverse axis.
\n" ); document.write( "Its standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of the center.
\n" ); document.write( "For given equation:(x+1)^2/4-(y-3)^2/4=1
\n" ); document.write( "center: (-1,3)
\n" ); document.write( "a^2=b^2=4
\n" ); document.write( "a=b=2
\n" ); document.write( "vertices: (-1±a,3)=(-1±2,3)=(-3,3) and (1,3)
\n" ); document.write( "..
\n" ); document.write( "foci:
\n" ); document.write( "c^2=a^2+b^2=4+4=8
\n" ); document.write( "c=√8≈2.8
\n" ); document.write( "foci: (-1±c,3)=(-1±2.8,3)=(-3.8,3) and (1.8,3)
\n" ); document.write( "..
\n" ); document.write( "Equations of Asymptotes:
\n" ); document.write( "Asymptotes are straight lines that go thru the center.
\n" ); document.write( "Slopes of asymptotes for hyperbolas with horizontal transverse axis=±b/a=±2/2=±1
\n" ); document.write( "Equation of asymptotes: y=±mx+b, m=slope, b=y-intercept
\n" ); document.write( "..
\n" ); document.write( "asymptote with negative slope:
\n" ); document.write( "y=-x+b
\n" ); document.write( "solve for b using (x,y) coordinates of center(-1,3)
\n" ); document.write( "3=1+b
\n" ); document.write( "b=2
\n" ); document.write( "equation: y=-x+2
\n" ); document.write( "..
\n" ); document.write( "asymptote with positive slope:
\n" ); document.write( "y=x+b
\n" ); document.write( "solve for b using (x,y) coordinates of center(-1,3)
\n" ); document.write( "3=-1+b
\n" ); document.write( "b=4
\n" ); document.write( "equation: y=x+4\r
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