大神的世界

拋物線頂點方程式

y = a(x-h)^2 + k

代入

=> y = a(x - x1)^2 + y1

a = (y2-y1)/(x2-x1)^2

=> (x2 - x1)^2 y = (y2 - y1)(x - x1)^2 + y1

(x2 - x1)^2 y = (y2 - y1)x^2 - 2x1(y2 - y1)x + (y2 - y1)x1^2 + y1

迴圈

輸入x1 y1 x2 y2

計算係數

約分

輸出

#include <iostream>
#include <algorithm>

using namespace std;

int main()
{
    int x1, x2, y1, y2;
    int a, b, c, d, gcd;

    while(cin >> x1 >> y1 >> x2 >> y2)
    {
        a = (x2-x1)*(x2-x1);
        b = y2-y1;
        c = -2*x1*(y2-y1);
        d = (y2-y1)*x1*x1 + y1*(x2-x1)*(x2-x1);

        gcd = __gcd(a, b), gcd = __gcd(gcd, c), gcd = __gcd(gcd, d);

        cout << a/gcd << "y = " << b/gcd << "x^2 + " << c/gcd << "x + " << d/gcd << endl;
    }
    return 0;
}