ZOJ3488-Conic Section

Conic Section

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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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.

conic sectionequationcirclex²+y²=a²ellipsex²/a²+y²/b²=1parabolay²=4axhyperbolax²/a²-y²/b²=1

Input

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.

Output

For each test case, output the type of conic section ax²+bxy+cy²+dx+ey+f=0. See sample for more details.

Sample Input

51 0 1 0 0 -11 0 2 0 0 -10 0 1 1 0 01 0 -1 0 0 12 0 2 4 4 0

Sample Output

circleellipseparabolahyperbolacircle

References

• Weisstein, Eric W. "Conic Section." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ConicSection.html

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Author: WU, Zejun
Contest: The 8th Zhejiang Provincial Collegiate Programming Contes

题意：给出方程 ax2+bxy+cy2+dx+ey+f=0 的系数，判断该曲线是圆，椭圆，双曲线还是抛物线。

#include <iostream>  #include <cstdio>  #include <string>  #include <cstring>  #include <algorithm>  #include <cmath>  #include <queue>  #include <vector>  #include <set>  #include <stack>  #include <map>  #include <climits>    using namespace std;    #define LL long long  const int INF=0x3f3f3f3f;    int main()  {      int t;      scanf("%d",&t);      while(t--)      {          double a,b,c,d,e,f;          scanf("%lf %lf %lf %lf %lf %lf",&a,&b,&c,&d,&e,&f);          if(a==c) printf("circle\n");          else if(a*c>0) printf("ellipse\n");          else if(a*c==0) printf("parabola\n");          else printf("hyperbola\n");      }      return 0;  }