ZOJ3488-Conic Section

B - Conic Section

Time Limit:2000MS     Memory Limit:65536KB     64bit IO Format:%lld & %llu

Submit  Status  Practice  ZOJ 3488

Description

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

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 <iostream>
#include <stdio.h>
#include <algorithm>

using namespace std;

int main()
{
    int n;
    scanf("%d",&n);
    while(n--)
    {
        double a,b,c,d,e,f;
        scanf("%lf%lf%lf%lf%lf%lf",&a,&b,&c,&d,&e,&f);
        if(a&&a==c&&d*d+e*e-4*c*f>0) printf("circle\n");
        else if(a*c<0&&((d*d/(4*a))+(e*e/(4*c))-f)!=0) printf("hyperbola\n");
        else if((!a&&d&&c)||(!c&&e&&a)) printf("parabola\n");
        else printf("ellipse\n");
    }
    return 0;
}