If you have taken a high-school level geometry course, then you have probably
encountered the concept of Parabolas. It is likely that you were taught
this information while learning about 2nd-degree polynomials and quadratic functions.
That is, taking plotting some function of the form f(x) = ax^2 + bx + c
will yield a parabola.
However, the actual geometric definition of a parabola may be unexpected or surprising
if you have only ever viewed them as plotted polynomials. First
select any focus point F, and then also some line D called the directrix.
The parabola is formed by the set (or locus) of all points which are equidistant
to both the focus and the directrix.
Note the pink lines indicating that any point on the parabola is equidistant both from the focus and from the directrix.
Problem Statement
Given the (x, y) coordinates of a focus point (fx, fy) and the equation of a
horizontal directrix given by the equation y = dy, find the 2nd-degree polynomial
which corresponds to the parabola defined.
Input Data
First line will be Q, the quantity of testcases.
Q lines will then follow, each with three space-separated values fx fy dy.
Answer
The answer to each testcase should consist of 3 space-separated values a b c,
corresponding to the 2nd-degree polynomial in the form f(x) = ax^2 + bx + c.
Full answer should consist of 3 * Q space-separated values total.
Error should be less than 1e-6.
Example
input data:
2
0 1 0
9.876 9.765 9.654
answer:
0.5 0 0.5 4.504505 -88.972973 449.058041