P为椭圆x^2/36+y^2/16=0的动点,过p作短轴的垂线,垂足为D,则PD的中点的轨迹方程是急
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![P为椭圆x^2/36+y^2/16=0的动点,过p作短轴的垂线,垂足为D,则PD的中点的轨迹方程是急](/uploads/image/z/12543295-31-5.jpg?t=P%E4%B8%BA%E6%A4%AD%E5%9C%86x%5E2%2F36%2By%5E2%2F16%3D0%E7%9A%84%E5%8A%A8%E7%82%B9%2C%E8%BF%87p%E4%BD%9C%E7%9F%AD%E8%BD%B4%E7%9A%84%E5%9E%82%E7%BA%BF%2C%E5%9E%82%E8%B6%B3%E4%B8%BAD%2C%E5%88%99PD%E7%9A%84%E4%B8%AD%E7%82%B9%E7%9A%84%E8%BD%A8%E8%BF%B9%E6%96%B9%E7%A8%8B%E6%98%AF%E6%80%A5)
P为椭圆x^2/36+y^2/16=0的动点,过p作短轴的垂线,垂足为D,则PD的中点的轨迹方程是急
P为椭圆x^2/36+y^2/16=0的动点,过p作短轴的垂线,垂足为D,则PD的中点的轨迹方程是
急
P为椭圆x^2/36+y^2/16=0的动点,过p作短轴的垂线,垂足为D,则PD的中点的轨迹方程是急
设 P(X,Y) M(m,n)
所以 D(X,0) M(X,Y/2)
故 X=m ,Y=2n
代入椭圆
m²/36+(2n)²/16=1
m²/36+n²/4=1
所以轨迹方程为
x²/36+y²/4=1