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a point P(a,b) is equidistant from the y axis and from the point (4,0). Find a relationship between a and b.

The book gives its answer as b^2 = 8a - 16

My problem is that the answer is correct, but I can't figure out the exact process they followed to reach it. Apart from plotting the points on a graph I am having difficulty trying to use the information in ways that don't end up looking ridiculous.

Can anyone offer some suggestions?