// Calculation Program for the minor axis of an egg body,
// 03 (Thur.) Dec., 2009

// egg equation: (x*x+y*y)**2=a*(x**3)+(a-b)*x*(y**2)

// The general condition needs b<=a,
// and in the case of b=0, the curve is led to a circle.

// file name: minor_axis.c

#include< stdio.h>
#include< math.h>

void main(void)
{
	double x,y,ypast,a,b,q,l2;
	double xmax,dx;

// Setting of the constants
	for(;;)
	{
		printf("Input of constant a; a= ? ");
		scanf("%lf",&a);
		if(a>0)
		{
			break;
		}
		else
		{
		printf("Please input the value of a after correcting a as a>0.\n");
		}
	}
	for(;;)
	{
		printf("Input of constant b; b= ? ");
		scanf("%lf",&b);
		if(b>=0&&b<=a)
		{
			break;
		}
		else
		{
printf("Pleease input the value of b after correcting b as 0< b < a or b=0 or b=a.\n");
		}
	}

	printf("\n");
	 
// Setting of the other parameters
	xmax=a;// maximum value of x
	dx=xmax/1000000;// minute increment of x

// execution of calculation
	ypast=-1;
	for(x=0;x<=xmax;x=x+dx)
	{
	y=sqrt(((a-b-2*x)+sqrt(4*b*x+(a-b)*(a-b)))*x/2);
		if(y< ypast)
		{
			q=ypast;
			break;
		}
		ypast=y;
	}

	l2=2*q;
	printf("The minor axis of the egg is; l2=%lf\n",l2);
	printf("\n");

	printf("end\n");
}// the end of the program