document.write( "Question 603270: Identify the conic section, re-write the equation in standard form, list the main characteristics, and graph
\n" ); document.write( "\"y%5E2-x%5E2%2B2x-6y%2B7=0\" \n" ); document.write( "
Algebra.Com's Answer #380718 by lwsshak3(11628)\"\" \"About 
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Identify the conic section, re-write the equation in standard form, list the main characteristics, and graph
\n" ); document.write( "y^2-x^2+2x-6y+7=0
\n" ); document.write( "complete the squares
\n" ); document.write( "(y^2-6y+9)-(x^2-2x+1)=-7+9-1
\n" ); document.write( "(y-3)^2-(x-1)^2=2
\n" ); document.write( "(y-3)^2/2-(x-1)^2/2=1
\n" ); document.write( "This is a hyperbola with vertical transverse axis.
\n" ); document.write( "Its standard form of equation: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center.
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "equation: (y-3)^2/2-(x-1)^2/2=1
\n" ); document.write( "Center: (1,3)
\n" ); document.write( "a^2=2
\n" ); document.write( "a=√2
\n" ); document.write( "length of vertical transverse axis=2a=2√2
\n" ); document.write( "b^2=2
\n" ); document.write( "b=√2
\n" ); document.write( "c^2=a^2+b^2=2+2=4
\n" ); document.write( "c=√4=2
\n" ); document.write( "Foci: (1, 3±c)=(1, 3±2)=(1, 1) and (1,5)\r
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