document.write( "Question 552369: Can you please show me the graph of 3x^2-2y^2+12x+4y+4=0 and the coordinates of the center and foci please! \n" ); document.write( "
Algebra.Com's Answer #360828 by lwsshak3(11628)\"\" \"About 
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Graph of 3x^2-2y^2+12x+4y+4=0
\n" ); document.write( "and the coordinates of the center and foci please!
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\n" ); document.write( "3x^2-2y^2+12x+4y+4=0
\n" ); document.write( "complete the square
\n" ); document.write( "3(x^2+4x+4)-2(y^2-2y+1)=-4+12-2
\n" ); document.write( "3(x+2)^2-2(y-1)^2=6
\n" ); document.write( "divide by 6
\n" ); document.write( "(x+2)^2/2-(y-1)^2/3=1
\n" ); document.write( "This 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) being the (x,y) coordinates of the center.
\n" ); document.write( "For given equation:
\n" ); document.write( "Center: (-2,1)
\n" ); document.write( "a^2=2
\n" ); document.write( "b^2=3
\n" ); document.write( "Foci:
\n" ); document.write( "c^2=a^2+b^2=2+3=5
\n" ); document.write( "c=√5≈2.24
\n" ); document.write( "Foci=(-2±c,1)=(-2±√5,1)=(-2±2.24,1)=(-4.24,1) and (.24,1)
\n" ); document.write( "see graph below as a visual check on the above:
\n" ); document.write( "y=±((3(x+2)^2/2)-3)^.5+1
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