document.write( "Question 1011076: Length of side of an equilateral triangle inscribed in a parabola y^2 -2x-2y-3=0 whose one angular point is vertex of the parabola \n" ); document.write( "
Algebra.Com's Answer #626707 by Alan3354(69443)\"\" \"About 
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Length of side of an equilateral triangle inscribed in a parabola y^2 -2x-2y-3=0 whose one angular point is vertex of the parabola
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\n" ); document.write( "The vertex is (-2,1)
\n" ); document.write( "The LOS of the parabola is y = 1
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\n" ); document.write( "Shift the parabola down 1 unit and right 2 units to the vertex is (0,0)
\n" ); document.write( "--> y^2 = 2x
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\n" ); document.write( "The angles of the sides of the vertex of the triangle are +30 degs and -30 degs wrt the x-axis.
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\n" ); document.write( "m1 = atan(30) = sqrt(3)/3
\n" ); document.write( "m2 = -sqrt(3)/3
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\n" ); document.write( "Equation of line with slope m1 thru (0,0) is
\n" ); document.write( "y = m1*x = x*sqrt(3)/3\r
\n" ); document.write( "\n" ); document.write( "x = y*sqrt(3)
\n" ); document.write( "Sub for x in y^2 = 2x
\n" ); document.write( "y^2 = 2y*sqrt(3)
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\n" ); document.write( "y^2 -2sqrt(3)y = 0
\n" ); document.write( "--> intersections at y = 0 (the vertex)
\n" ); document.write( "and at y = 2sqrt(3)
\n" ); document.write( "--> 1/2 side length = 2sqrt(3)
\n" ); document.write( "sides = 4sqrt(3)
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