已知定点M(-3,4),动点N在圆x^2+y^2=4上运动,O为坐标原点,以OM,ON为边做平行四边形MONP,求点P的轨迹方程向量MP=向量ON N(x1,y1) P(x,y) x+3=x1;y-4=y1 代入,得 (x+3)^2+(y-4)^2=4 当N在直线OM上时不可行.即(±6/5,±8/
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 18:34:02
![已知定点M(-3,4),动点N在圆x^2+y^2=4上运动,O为坐标原点,以OM,ON为边做平行四边形MONP,求点P的轨迹方程向量MP=向量ON N(x1,y1) P(x,y) x+3=x1;y-4=y1 代入,得 (x+3)^2+(y-4)^2=4 当N在直线OM上时不可行.即(±6/5,±8/](/uploads/image/z/6086901-21-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9A%E7%82%B9M%28-3%2C4%29%2C%E5%8A%A8%E7%82%B9N%E5%9C%A8%E5%9C%86x%5E2%2By%5E2%3D4%E4%B8%8A%E8%BF%90%E5%8A%A8%2CO%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%2C%E4%BB%A5OM%2CON%E4%B8%BA%E8%BE%B9%E5%81%9A%E5%B9%B3%E8%A1%8C%E5%9B%9B%E8%BE%B9%E5%BD%A2MONP%2C%E6%B1%82%E7%82%B9P%E7%9A%84%E8%BD%A8%E8%BF%B9%E6%96%B9%E7%A8%8B%E5%90%91%E9%87%8FMP%3D%E5%90%91%E9%87%8FON+N%28x1%2Cy1%29+P%28x%2Cy%29+x%2B3%3Dx1%3By-4%3Dy1+%E4%BB%A3%E5%85%A5%2C%E5%BE%97+%28x%2B3%29%5E2%2B%28y-4%29%5E2%3D4+%E5%BD%93N%E5%9C%A8%E7%9B%B4%E7%BA%BFOM%E4%B8%8A%E6%97%B6%E4%B8%8D%E5%8F%AF%E8%A1%8C.%E5%8D%B3%28%C2%B16%2F5%2C%C2%B18%2F)
已知定点M(-3,4),动点N在圆x^2+y^2=4上运动,O为坐标原点,以OM,ON为边做平行四边形MONP,求点P的轨迹方程向量MP=向量ON N(x1,y1) P(x,y) x+3=x1;y-4=y1 代入,得 (x+3)^2+(y-4)^2=4 当N在直线OM上时不可行.即(±6/5,±8/
已知定点M(-3,4),动点N在圆x^2+y^2=4上运动,O为坐标原点,以OM,ON为边做平行四边形MONP,求点P的轨迹方程
向量MP=向量ON
N(x1,y1)
P(x,y)
x+3=x1;y-4=y1
代入,得
(x+3)^2+(y-4)^2=4
当N在直线OM上时不可行.即(±6/5,±8/5)
x+3≠±6/5,
x≠-9/5且x≠-21/5
综上,P的轨迹方程为
(x+3)^2+(y-4)^2=4,x≠-9/5且x≠-21/5
(x≠-9/5且x≠-21/5)怎么求的?
已知定点M(-3,4),动点N在圆x^2+y^2=4上运动,O为坐标原点,以OM,ON为边做平行四边形MONP,求点P的轨迹方程向量MP=向量ON N(x1,y1) P(x,y) x+3=x1;y-4=y1 代入,得 (x+3)^2+(y-4)^2=4 当N在直线OM上时不可行.即(±6/5,±8/
画图,
由A(-3,4)与O(0,0,)易求得直线AO:y=-4x/3,
带入圆方程,x²+(-4x/3)²=4,即x=6/5或x=-6/5,
这两点为直线AC与圆的两个交点的横坐标,
欲构成平行四边形,N点就不能与这两点重合,
即x₁≠6/5且x₁≠-6/5,
而P点横坐标x=x₁-3,即x≠6/5-3=-9/5且x≠-6/5-3=-21/5.