An oscillating circle is a circle which is tangent to a curve at some point P,
and also has the same curvature of the curve at that point P. If our curve is
a parabola and our point P is at the vertex of the parabola (the point on the
parabola closest to the directrix), then we can observe that the osculating circle
fits very nicely inside that curve. In fact if the circle had just a slightly larger
radius, then it would be too big to reach the point P. We could gradually decrease
that radius until the exact moment that our circle "kisses" the point P, which yields
the parabolic osculating circle. Such a metaphor is appropriate, as "ōsculātus" is Latin for
"kissed".
The parabola defined by the function f(x) = x^2 is shown in Blue.
On the left in Purple is the associated osculating circle.
On the right in Red is a circle too large to "kiss" the point P.
Problem Statement
Input Data
First line will be Q, the quantity of testcases.
Q lines will follow, each with three space-separated values a b c, describing
a polynomial in the form a * x^2 + b * x + c.
Answer
Should consist of 2 * Q space-separated values, corresponding to the (x, y)
coordinates of the osculating circle's centerpoint in each testcase.
Error should be less than 1e-6.
Example
input data:
2
1 0 0
-9.8 7.6 -5.4
answer:
0 0.5 0.387755 -3.977551