已知直线L:y=x+1与曲线C:x^2/a^2+y^2/b^2=1(a>0,b>0)交于不同的两点A,B,O为坐标原点.(1)若OA的绝对值=OB的绝对值,求证:曲线C是一个圆(2)若OA垂直OB,当a>b且a∈[(√6)/2,(√10)/2]时,求曲线C的
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![已知直线L:y=x+1与曲线C:x^2/a^2+y^2/b^2=1(a>0,b>0)交于不同的两点A,B,O为坐标原点.(1)若OA的绝对值=OB的绝对值,求证:曲线C是一个圆(2)若OA垂直OB,当a>b且a∈[(√6)/2,(√10)/2]时,求曲线C的](/uploads/image/z/10006159-31-9.jpg?t=%E5%B7%B2%E7%9F%A5%E7%9B%B4%E7%BA%BFL%EF%BC%9Ay%3Dx%2B1%E4%B8%8E%E6%9B%B2%E7%BA%BFC%EF%BC%9Ax%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%28a%3E0%2Cb%3E0%29%E4%BA%A4%E4%BA%8E%E4%B8%8D%E5%90%8C%E7%9A%84%E4%B8%A4%E7%82%B9A%2CB%2CO%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9.%EF%BC%881%EF%BC%89%E8%8B%A5OA%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%3DOB%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%2C%E6%B1%82%E8%AF%81%EF%BC%9A%E6%9B%B2%E7%BA%BFC%E6%98%AF%E4%B8%80%E4%B8%AA%E5%9C%86%EF%BC%882%EF%BC%89%E8%8B%A5OA%E5%9E%82%E7%9B%B4OB%2C%E5%BD%93a%3Eb%E4%B8%94a%E2%88%88%5B%EF%BC%88%E2%88%9A6%EF%BC%89%2F2%2C%EF%BC%88%E2%88%9A10%EF%BC%89%2F2%5D%E6%97%B6%2C%E6%B1%82%E6%9B%B2%E7%BA%BFC%E7%9A%84)
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