SOLUTION: Please help me with those problems. Thanks!!!!! 1)Graph x2 + 2xy + y2 = 1. 2)If the parabola defined by y = ax^2 + 6 is tangent to the line y = x, then calculate the constant a.

Question 477245: Please help me with those problems. Thanks!!!!!
1)Graph x2 + 2xy + y2 = 1.
2)If the parabola defined 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.)
3)Find a complex number whose square equals i.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
1)
<==>
<==> (x+y-1)(x+y + 1) = 0.
The graph is the union of the two lines y = -x + 1 and y = -x - 1.

2) Solve for the system y = x and such that there is only one point of intersection.
==> Let ==>
For there to be only one point of intersection, the discriminant has to be equal to 0.
==> , or 1- 24a = 0, or .
3) Let . Since ,
we have
Hence we can let , or
.
thus a complex number whose square is i is
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SOLUTION: Please help me with those problems. Thanks!!!!! 1)Graph x2 + 2xy + y2 = 1. 2)If the parabola de fined by y = ax^2 + 6 is tangent to the line y = x, then calculate the constant a.

SOLUTION: Please help me with those problems. Thanks!!!!! 1)Graph x2 + 2xy + y2 = 1. 2)If the parabola defined by y = ax^2 + 6 is tangent to the line y = x, then calculate the constant a.