js椭圆和直线交点坐标

function getEllipseLineIntersection(h, k, a, b, m, c) {
    // 将直线方程 y = mx + c 代入椭圆方程
    let A = b*b + a*a*m*m;
    let B = 2*a*a*m*c - 2*a*a*m*k - 2*b*b*h;
    let C = b*b*h*h + a*a*c*c - 2*a*a*c*k + a*a*k*k - a*a*b*b;

    // 计算二次方程的判别式
    let discriminant = B*B - 4*A*C;

    if (discriminant < 0) {
        return []; // 无交点
    } else if (discriminant === 0) {
        let x = -B / (2*A);
        let y = m*x + c;
        return [[x, y]]; // 一个交点
    } else {
        let x1 = (-B + Math.sqrt(discriminant)) / (2*A);
        let x2 = (-B - Math.sqrt(discriminant)) / (2*A);
        let y1 = m*x1 + c;
        let y2 = m*x2 + c;
        return [[x1, y1], [x2, y2]]; // 两个交点
    }
}

// 使用示例
let h = 0, k = 0; // 椭圆中心
let a = 5, b = 3; // 椭圆半轴
let m = 1, c = -3; // 直线斜率和截距
console.log(getEllipseLineIntersection(h, k, a, b, m, c));