直线L:y=kx+b与椭圆x²/2+y²=1交于P、Q两点,且OP与OQ垂直(O为坐标原点),求证:直线L与原点的距离为常数,并求出这个常数.
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![直线L:y=kx+b与椭圆x²/2+y²=1交于P、Q两点,且OP与OQ垂直(O为坐标原点),求证:直线L与原点的距离为常数,并求出这个常数.](/uploads/image/z/3994205-5-5.jpg?t=%E7%9B%B4%E7%BA%BFL%EF%BC%9Ay%3Dkx%2Bb%E4%B8%8E%E6%A4%AD%E5%9C%86x%26sup2%3B%2F2%2By%26sup2%3B%3D1%E4%BA%A4%E4%BA%8EP%E3%80%81Q%E4%B8%A4%E7%82%B9%2C%E4%B8%94OP%E4%B8%8EOQ%E5%9E%82%E7%9B%B4%EF%BC%88O%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%EF%BC%89%2C%E6%B1%82%E8%AF%81%EF%BC%9A%E7%9B%B4%E7%BA%BFL%E4%B8%8E%E5%8E%9F%E7%82%B9%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA%E5%B8%B8%E6%95%B0%2C%E5%B9%B6%E6%B1%82%E5%87%BA%E8%BF%99%E4%B8%AA%E5%B8%B8%E6%95%B0.)
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