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Given the parabola y = x & # 178, the angle between the tangent line at the upper point P and the straight line y = 3x + 1 is 45 ° and the coordinates of point P are obtained
Let P (a, a & # 178;)
The derivative of y = x & # is y = 2x
The slope of the tangent at P is 2A
The slope of the line y = 3x + 1 is 3
From the angle formula, we can get | (2a-3) / (1 + 6a) | = tan45 ° = 1
That is, (2a-3) / (1 + 6a) = 1 or (2a-3) / (1 + 6a) = - 1
The solution is a = - 1 or a = 1 / 4
So p (- 1,1) or (1 / 4,1 / 16)
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