点p为双曲线x²/4-y²=1上一动点,o为坐标原点,m为线段op中点,则点m的轨迹方程是
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![点p为双曲线x²/4-y²=1上一动点,o为坐标原点,m为线段op中点,则点m的轨迹方程是](/uploads/image/z/8632680-24-0.jpg?t=%E7%82%B9p%E4%B8%BA%E5%8F%8C%E6%9B%B2%E7%BA%BFx%26%23178%3B%2F4-y%26%23178%3B%3D1%E4%B8%8A%E4%B8%80%E5%8A%A8%E7%82%B9%2Co%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%2Cm%E4%B8%BA%E7%BA%BF%E6%AE%B5op%E4%B8%AD%E7%82%B9%2C%E5%88%99%E7%82%B9m%E7%9A%84%E8%BD%A8%E8%BF%B9%E6%96%B9%E7%A8%8B%E6%98%AF)
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点p为双曲线x²/4-y²=1上一动点,o为坐标原点,m为线段op中点,则点m的轨迹方程是
点p为双曲线x²/4-y²=1上一动点,o为坐标原点,m为线段op中点,则点m的轨迹方程是
点p为双曲线x²/4-y²=1上一动点,o为坐标原点,m为线段op中点,则点m的轨迹方程是
解设P(x1,y1),M(x,y)
由m为线段op中点
则x=(x1+0)/2,y=(y1+0)/2
即x1=2x,y1=2y
由p为双曲线x^2/4-y^2=1上一动点
即x1^2/4-y1^2=1
即(2x)^2/4-(2y)^2=1
即x^2-4y^2=1
故点m的轨迹方程是x^2-4y^2=1.