ZOJ - 3488 Conic Section

Conic Section

---

Time Limit: 2 Seconds      Memory Limit: 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.

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

---

Author: WU, Zejun

Contest: The 8th Zhejiang Provincial Collegiate Programming Contest

看起来很可怕的一道题，其实很简单，不过是在高中知识还在的情况下，哈哈哈，我可是查了相关的定义才做出来的，太差了太差了

abcdef其实是有联系的，具体判定方法还是自行百度吧。

#include <iostream>#include <cstdio>#include <cstring>#include <string>using namespace std;int T;double a,b,c,d,e,f;int main(){    cin>>T;    while(T--)    {        cin>>a>>b>>c>>d>>e>>f;        if(b*b-4*a*c<0)        {            if(a==c&&(d*d+e*e-4*f>0))                cout<<"circle"<<endl;            else                cout<<"ellipse"<<endl;        }           else if(b*b-4*a*c==0)            cout<<"parabola"<<endl;        else if(b*b-4*a*c>0)            cout<<"hyperbola"<<endl;    }    return 0;}