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
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#include<stdio.h> int main() { int t; double a,b,c,d,e,f; while(scanf("%d",&t)!=EOF) { while(t--) { 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; }