document.write( "Question 971565: Identify the conic section. if it is a parabola, give the vertex. if it is a circle, give the center and radius. if it is an ellipse or hyperbola, give the center and foci.
\n" ); document.write( "a) 6x^2 - 5y^2 + 12x - 10y - 3 = 0\r
\n" ); document.write( "\n" ); document.write( "b) 4x^2 + 3y^2 - 8x + 6y = 2
\n" ); document.write( "

Algebra.Com's Answer #594030 by lwsshak3(11628)\"\" \"About 
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Identify the conic section. if it is a parabola, give the vertex. if it is a circle, give the center and radius. if it is an ellipse or hyperbola, give the center and foci.
\n" ); document.write( "a) 6x^2 - 5y^2 + 12x - 10y - 3 = 0
\n" ); document.write( "6x^2+ 12x - 5y^2 - 10y=3
\n" ); document.write( "complete the square:
\n" ); document.write( "6(x^2+2x+1) - 5( y^2+2y+1)=3+6-5
\n" ); document.write( "6(x+1)^2-5((y+1)^2=4
\n" ); document.write( "\"%28x%2B1%29%5E2%2F%284%2F6%29-%28y%2B1%29%5E2%2F%284%2F5%29=1\"
\n" ); document.write( "This is an equation of a hyperbola with horizontal transverse axis
\n" ); document.write( "Its standard form of equation: \"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"
\n" ); document.write( "center: (-1, -1)
\n" ); document.write( "a^2=4/6=2/3
\n" ); document.write( "b^2=4/5
\n" ); document.write( "foci:
\n" ); document.write( "c^2=a^2+b^2=2/3+4/5=10/15+12/15=22/15
\n" ); document.write( "c=√(22/15)≈1.2
\n" ); document.write( "foci: (-1±c,-1)=(-1±1.2,-1)+(-2.2,-1) and (0.2, -1)
\n" ); document.write( "..
\n" ); document.write( "b) 4x^2 + 3y^2 - 8x + 6y = 2
\n" ); document.write( "4x^2- 8x + 3y^2 + 6y = 2
\n" ); document.write( "complete the square:
\n" ); document.write( "4(x^2- 2x+1) + 3(y^2 + 2y+1) = 2+4+3
\n" ); document.write( "4(x-1)^2+3(y+1)^2=9
\n" ); document.write( "\"%28x-1%29%5E2%2F%289%2F4%29%2B%28y%2B1%29%5E2%2F3=1\"
\n" ); document.write( "This is an equation of an ellipse with vertical major axis
\n" ); document.write( "Its standard form of equation: \"%28x-h%29%5E2%2Fb%5E2-%28y-k%29%5E2%2Fa%5E2=1\"
\n" ); document.write( "center: (1,-1)
\n" ); document.write( "a^2=3
\n" ); document.write( "b^2=(9/4)
\n" ); document.write( "c^2=a^2-b^2=9-9/4=36/4-9/4=27/4
\n" ); document.write( "c=√(27/4)=2.6
\n" ); document.write( "foci: (1,-1±c)=(1.-1±2.6)=(1,-3.6) and (1,1.6)
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