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It is known that circle C: x2 + (Y-1) 2 = 5, straight line L: mx-y + 1-m = 0 (1) Judge the position relationship between line L and circle C (2) If the line L intersects the circle C at points a and B, and the length of AB is the smallest, the value of M is obtained It's (Y-2) 2. I was inspired by what I did on the second floor. Is m equal to 1 when Y-2?
1. Mx-y + 1-m = 0 (x-1) M-Y + 1 = 0, the straight line L passes through the fixed point (1,1), substituting x ^ 2 + (Y-1) ^ 2 < 5, so the fixed point is in the circle, that is, the straight line L intersects the circle C. 2. Let the center of the circle be D, and the fixed point (1,1) be e. obviously, when de ⊥ L, AB is the shortest (because the radius is fixed, the greater the distance from the point to the straight line, the smaller the chord length, Pythagorean theorem)
RELATED INFORMATIONS
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