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

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