M(x,y)在圆x^2+y^2=1上移动,求点Q(x(x+y),y(x+y))的轨迹_数学解答

M(x,y)在圆x^2+y^2=1上移动,求点Q(x(x+y),y(x+y))的轨迹

人气：289 ℃　时间：2020-06-23 18:47:24

解答

用参数方程来表示简单些.设 M(x,y) 圆的参数方程：x=cost,y=sint Q点坐标x=cost(cost+sint)=cos^2t+cost*sint=1/2*cos2t+1/2+1/2*sin2t= √2/2 (√2/2*cost2t + √2/2*sin2t)+1/2= √2/2 cost(2t-π/4)+1/2y=sint(co...