document.write( "Question 477245: Please help me with those problems. Thanks!!!!!
\n" ); document.write( "1)Graph x2 + 2xy + y2 = 1.
\n" ); document.write( "2)If the parabola de fined by y = ax^2 + 6 is tangent to the line y = x, then calculate the constant a. (A line is tangent to a parabola if it touches the parabola at one point, but is otherwise always \"outside\" the parabola.)
\n" ); document.write( "3)Find a complex number whose square equals i. \n" ); document.write( "
Algebra.Com's Answer #327186 by robertb(5830)\"\" \"About 
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1) \"x%5E2+%2B+2xy+%2B+y%5E2+=+1\"
\n" ); document.write( "<==> \"%28x%2By%29%5E2+-+1+=+0\"
\n" ); document.write( "<==> (x+y-1)(x+y + 1) = 0.\r
\n" ); document.write( "\n" ); document.write( "The graph is the union of the two lines y = -x + 1 and y = -x - 1.\r
\n" ); document.write( "\n" ); document.write( "\"graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+-x-1%2C+-x+%2B1%29\"\r
\n" ); document.write( "\n" ); document.write( "2) Solve for the system y = x and \"y+=+ax%5E2+%2B+6\" such that there is only one point of intersection.
\n" ); document.write( "==> Let \"+x+=+ax%5E2+%2B+6\" ==> \"ax%5E2+-+x+%2B+6+=+0\"
\n" ); document.write( "For there to be only one point of intersection, the discriminant has to be equal to 0.
\n" ); document.write( "==> \"%28-1%29%5E2+-+4%2Aa%2A6+=+0\", or 1- 24a = 0, or \"a+=+1%2F24\".\r
\n" ); document.write( "\n" ); document.write( "3) Let \"x+=+e%5E%28i%2Atheta%29\". Since \"i+=+e%5E%28%281%2F2%29%2Ai%2Api%29\", \r
\n" ); document.write( "\n" ); document.write( "we have \"%28e%5E%28i%2Atheta%29%29%5E2+=+e%5E%282i%2Atheta%29+=+e%5E%28%281%2F2%29%2Ai%2Api%29\"
\n" ); document.write( "Hence we can let \"2i%2Atheta+=+%28i%2F2%29%2Api\", or
\n" ); document.write( "\"theta+=+pi%2F4\".
\n" ); document.write( "thus a complex number whose square is i is \n" ); document.write( "
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