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Find a point P on the parabola y ^ 2 = 4x, so that the distance from point P to the straight line y = x + 3 is the shortest
This proposition can be transformed into finding the tangent point between a straight line y = x + B parallel to y = x + 3 and a parabola y ^ 2 = 4x. At this time, the distance between the point P and the straight line y = x + 3 is the shortest (drawing is more intuitive). The simultaneous equation y = x + B, y ^ 2 = 4x, x ^ 2 + (2b-4) x + B ^ 2 = 0, Δ = 0, (2b-4) ^ 2-4b ^ 2 = 0, B = 1, so, x = 1, y = 2
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