ZOJ 3488Conic 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 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

简单题，先判断是否椭圆或圆，再判断是否双曲线即可

#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;}