Time Limit: Java: 2000 ms / Others: 2000 ms
Memory Limit: Java: 65536 KB / Others: 65536 KB
The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, a circle is produced. For a plane that is not perpendicular to the axis and that intersects only a single nappe, the curve produced is either an ellipse or a parabola. The curve produced by a plane intersecting both nappes is a hyperbola.
There are multiple test cases. The first line of input is an integer T ≈ 10000 indicating the number of test cases.
Each test case consists of a line containing 6 real numbers a, b, c, d, e, f. The absolute value of any number never exceeds 10000. It's guaranteed that a2+c2>0, b=0, the conic section exists and it is non-degenerate.
For each test case, output the type of conic section ax2+bxy+cy2+dx+ey+f=0. See sample for more details.
circle ellipse parabola hyperbola circle References Weisstein, Eric W. "Conic Section." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ConicSection.html