已知动圆M与圆C1:(x+4)²+y²=2外切,与圆C2:(x-4)²+y²=2内切,求动圆圆心M的轨迹方程.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/13 01:17:34
![已知动圆M与圆C1:(x+4)²+y²=2外切,与圆C2:(x-4)²+y²=2内切,求动圆圆心M的轨迹方程.](/uploads/image/z/4495128-24-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%8A%A8%E5%9C%86M%E4%B8%8E%E5%9C%86C1%3A%28x%2B4%29%26%23178%3B%2By%26%23178%3B%3D2%E5%A4%96%E5%88%87%2C%E4%B8%8E%E5%9C%86C2%3A%28x-4%29%26%23178%3B%2By%26%23178%3B%3D2%E5%86%85%E5%88%87%2C%E6%B1%82%E5%8A%A8%E5%9C%86%E5%9C%86%E5%BF%83M%E7%9A%84%E8%BD%A8%E8%BF%B9%E6%96%B9%E7%A8%8B.)
x){}Kvx:Ɏ> lhQmlhna] m.]HVg ffZ^]bgv>_ѭgT?`vk|
kF5Et=edtݬ
{ 1yN$#f{Fg';v=oYF@ػiϳٛfo~6e}6=^'*04K"h-PQ}#745TШ3д/.H̳- i'
已知动圆M与圆C1:(x+4)²+y²=2外切,与圆C2:(x-4)²+y²=2内切,求动圆圆心M的轨迹方程.
已知动圆M与圆C1:(x+4)²+y²=2外切,与圆C2:(x-4)²+y²=2内切,求动圆圆心M的轨迹方程.
已知动圆M与圆C1:(x+4)²+y²=2外切,与圆C2:(x-4)²+y²=2内切,求动圆圆心M的轨迹方程.
|MC1|-|MC2|=r1+r2=2√2=定值
则点M的轨迹是以C1、C2为焦点、以2a=2√2为实轴的双曲线的右支,得:
a=√2,c=4,得:b=√14
轨迹方程是:x²/2-y²/14=1 (x>0)