Question

从椭圆x^2/2+y^2=1上一点Q引直线l:x+y=2的垂线,垂足为N求线段QN的中点P的轨迹方程

从椭圆x^2/2+y^2=1上一点Q引直线l:x+y=2的垂线，垂足为N求线段QN的中点P的轨迹方程

Answer 1

(y-yN)/(x-xN)=-1/k(L)=1
xN-yN=x-y......(1)
xN+yN=2......(2)
xN=1+0.5x-0.5y
yN=1-0.5x+0.5y
P(x,y)
xQ+xN=2x,xQ=2x-xN=2x-(1+0.5x-0.5y)=1.5x+0.5y-1
yQ+yN=2y,yQ=2y-yN=2y-(1-0.5x+0.5y)=0.5x+1.5y-1
(xQ)^2/2+(yQ)^2=1
(1.5x+0.5y-1)^2/2+(0.5x+1.5y-1)^2=1