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显示全部楼层 · 2009-8-25 13:46:40

设N(u,v),则OM方程为：y=vx/u设：M(w,vw/u)则：√(u^2+v^2)√(w^2+(vw/u)^2=w(u^2+v^2)/u=150w=150u/(u^2+v^2)所以，M(150u/(u^2+v^2),150v^2/(u^2+v^2))所以(150u/(u^2+v^2))^2+(150v/(u^2+v^2))^2-6(150u/(u^2+v^2))-8(150v/(u^2+v^2))=0即：150u^2/(u^2+v^2)+150v^2/(u^2+v^2)-6u-8v=0150-6u-8v=03u+4v=50所以，N的轨迹方程是：3x+4y=50...

千问 · 2009-8-25 13:46:40

x^2+y^2-6x-8y=0推出(x-3)^2+(y-4)^2=25知M是以点O(3,4)为圆心，5为半径的圆周点，所以|OM|=5，|ON|=30点N的轨迹是以O（3，4）为圆心30为半径的圆，方程(x-3)^2+(y-4)^2=900，化简X^2+Y^2-6X-8Y-875=0...