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题176已知过椭圆C:xb22+by22=1(ab0)右焦点F且斜率为1的直线交椭圆C于A,B两点,N为弦AB的中点;又函数y=a·sinx+3b·cosx的图象的一条对称轴的方程是x=6π.1)求椭圆C的离心率e与kON;2)对于任意一点M∈C,试证:总存在角θ(θ∈R)使等式:OM=cosθOA+sinθOB成立.解1)函数y=a·sin
Problem 176 It is known that the ellipse C: xb22 + by22 = 1 (ab0) the right focus F and the slope of the line 1 is a cross-oval C with two points A and B, where N is the midpoint of the string AB; and the function y=a·sinx The equation of an axis of symmetry of the image of +3b·cosx is x=6π.1) find the eccentricity e and kON of the ellipse C; 2) for any point M∈C, test: the total existence angle θ (θ∈R ) Let the equation: OM = cosθOA + sinθ OB be established. Solution 1) Function y = a · sin