已知椭圆x^2/4+y^2=1,过点M（2,3）引直线交椭圆于A,B两点,求弦AB的中点P的轨迹方程

P(x,y)
xA+xB=2x,yA+yB=2y
k(AB)=(yA-yB)/(xA-xB)=(yP-yM)/(xP-xM)=(y-3)/(x-2)
x^2/4+y^2=1
(xA)^2/4+(yA)^2=1.(1)
(xA)^2/4+(yB)^2=1.(2)
(1)-(2):
(xA+xB)*(xA-xB)/4+(yA+yB)*(yA-yB)=0
(xA+xB)+4(yA+yB)*(yA-yB)/(xA-xB)=0
2x+4*2y*(y-3)/(x-2)=0
AB的中点P的轨迹方程椭圆:(x-1)^2/10+(y-1.5)^2/2.5=1