document.write( "Question 479772: Can you please put this equation into the standard form of a conic, step-by-step?\r
\n" ); document.write( "\n" ); document.write( "3y^2 + 20x = 23 + 5x^2 + 12y \n" ); document.write( "
Algebra.Com's Answer #328724 by lwsshak3(11628)\"\" \"About 
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Can you please put this equation into the standard form of a conic, step-by-step?
\n" ); document.write( "3y^2 + 20x = 23 + 5x^2 + 12y
\n" ); document.write( "**
\n" ); document.write( "3y^2 + 20x = 23 + 5x^2 + 12y
\n" ); document.write( "3y^2- 12y - 5x^2+ 20x = 23
\n" ); document.write( "complete the square
\n" ); document.write( "3(y^2-4y+4)-5(x^2-4x+4)=23+12-20=15
\n" ); document.write( "3(y-2)^2-5(x-2)^2=15
\n" ); document.write( "divide by 15
\n" ); document.write( "(y-2)^2/5-(x-2)^2/3=1
\n" ); document.write( "This is an equation of a hyperbola with vertical transverse axis of the standard form:
\n" ); document.write( "(y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the center of the hyperbola.
\n" ); document.write( "For given equation:
\n" ); document.write( "Center: (2,2)
\n" ); document.write( "a^2=5
\n" ); document.write( "a=√5
\n" ); document.write( "length of transverse axis=2a=2√5=4.47
\n" ); document.write( "b^2=3
\n" ); document.write( "b=√3
\n" ); document.write( "length of conjugate axis=2b=2√3=3.46 \n" ); document.write( "
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