ZOJ 3488 Conic Section

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 section	equation
circle	x2+y2=a2
ellipse	x2/a2+y2/b2=1
parabola	y2=4ax
hyperbola	x2/a2-y2/b2=1

Input

There are multiple test cases. The first line of input is an integer T

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

5
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 Output

circle
ellipse
parabola
hyperbola
circle      

References

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

#include<map>
#include<cmath>    
#include<queue> 
#include<string>
#include<vector>
#include<cstdio>    
#include<cstring>  
#include<iostream>
#include<algorithm>    
using namespace std;
#define ms(x,y) memset(x,y,sizeof(x))    
#define rep(i,j,k) for(int i=j;i<=k;i++)    
#define per(i,j,k) for(int i=j;i>=k;i--)    
#define loop(i,j,k) for (int i=j;i!=-1;i=k[i])    
#define inone(x) scanf("%d",&x)    
#define intwo(x,y) scanf("%d%d",&x,&y)    
#define inthr(x,y,z) scanf("%lf%lf%lf",&x,&y,&z)    
typedef long long LL;
const int low(int x) { return x&-x; }
const int INF = 0x7FFFFFFF;
const int mod = 1e9 + 7;
const int N = 1e5 + 10;
int T, n;
double a, b, c, d, e, f;

int main()
{
  for (inone(T); T--;)
  {
    inthr(a, b, c); inthr(d, e, f);
    if (a * c > 0) puts(a == c ? "circle" : "ellipse");
    else puts(a*c ? "hyperbola" : "parabola");
  }
  return 0;
}