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## Main Question or Discussion Point

Hi all (<--new user) I've spent the last 6 months trying to learn A-level mathematics in a vacuum after 9 years of letting my GCSE knowledge slide into oblivion, this is the first time however, I've hit a question for which how the book arrives at its answer is completely frying my brain. The question (the last of 12 questions) is as follows:

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?

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?