ZOJ3488-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 ≈ 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, ZejunContest: The 8th Zhejiang Provincial Collegiate Programming Contest
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 longconst 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;}