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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.
Any hints on how to go about this appreciated.
Thanks.
Any hints on how to go about this appreciated.
Thanks.
That's the basic idea but I see no reason to introduce "Q". The distance from (a, b) to the y-axis is the distance from (a, b) to (0, b) and is equal to |a|. The distance from (a, b) to (4, 0) is [itex]\sqrt{(a- 4)^2+ b^2}[/itex]. (a, b) is "equidistant from the y-axis and (4, 0)" if and only if those are equal:Hi,
I've tried numerous ways of tackling this but I can't seem to get the answer that I have in my solutions booklet. Looking to see if anyone can give an alternative starting. Anyway here's one approach I used...
Let Q be the point the line A(4, 0) -> P(a, b) cuts the y-axis.
[tex]AP^2 = (4 - a)^2 + b^2[/tex]
[tex]PQ^2 = a^2 + (b - (4b/(4-a)))^2[/tex]
but [tex]AP^2=PQ^2[/tex]. In trying to simplify that I get something that isn't even close... which is:
[tex](b^2(6-a))/((4-a)^2) = 2 - a[/tex]
Thanks.