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Which tangent point is shortest line segment?

Hello everyone. I have this problem, (problem 2 on the worksheet), that I am having trouble understanding. Could anyone shed any light. I am getting confused as to what the positive point C is supposed to be. Any advice will be appreciated. Thank You.

Re: Which tangent point is shortest line segment?

Hey marsalanuddin.

The first suggestion I have is to find a way of finding the intercept of the line with the x-axis and then use this to get your distance function.

We know that for a straight-line y = 0 so given y = mx + b this means that x = -b/m where m is the slope of the tangent.

Also minimizing d^2 will minimize d (i.e. the distance function).

So your line will be from (-b/m,0) to (x,y(x)) for some tangent line, so try finding a minimization problem given that x > 0