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    Shortest Length of Line Intersection

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    If P is any point on the parabola y = x^2 except for the origin, let Q be the point where the normal line intersects the parabola again. Find the shortest possible length of the line segment PQ.

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    https://brainmass.com/math/graphs-and-functions/shortest-length-line-intersection-25485

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    See attachment please!

    If P is any point on the parabola y = x^2 except for the origin, let Q be the point where the normal line intersects the parabola again. Find the shortest possible length of the line segment PQ.

    Solution. Suppose that is a point on the parabola except for the origin. So we have

    Now we know that the tangent line L at P(a,b) can be determined as follows. First, the slope of L is

    So, we can get the slope of the normal line L' at P(a,b) as follows.
    ...

    Solution Summary

    This shows how to find the shortest possible length of a segment from a parabola to an intersection with the normal line.

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