
ZOJ Problem Set  3488
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.
InputThere 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 a^{2}+c^{2}>0, b=0, the conic section exists and it is nondegenerate. OutputFor each test case, output the type of conic section ax^{2}+bxy+cy^{2}+dx+ey+f=0. See sample for more details. Sample Input5 1 0 1 0 0 1 1 0 2 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 2 0 2 4 4 0 Sample Outputcircle ellipse parabola hyperbola circle References
Author: WU, Zejun Contest: The 8th Zhejiang Provincial Collegiate Programming Contest 