Loci help (1)

A and B are two points that are exactly 5cm apart. PLot the locus of the point P such that AP + PB = 9cm.


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I had an attempt at it. The way I did it was by drawing a circle with a radius of 4.5cm on the midpoint of A and B. It was almost correct (not really). The answer is an eclipse. Could anyone please explain why though? MANY THANKS!!

A circle is the locus of a point that is a constant distance from a single point.

An ellipse is the locus of a point whose sum of distances from two fixed points is constant.
Have you ever put two drawing pins in a piece of paper, then looped a string loosely round the pair, taken a pen(cil) and drawn the position of the points with the string stretched - if not, have a go.

thank you for your help!
i was just wondering, say i got this question in an exam, but i can't use any stings/pins or any of those equipment - what do i do?

Firstly you need to recognise that a number can be made up of two other numbers and not just equidistant. You have to use your powers of visualisation a little more and think 1+8=9, 2+7=9, etc..etc.. They using your compass plot these points relative to A and B and eventually you'll get all the points. Obviously, you're not expected, nor would you have the time, to mark every singly point but after a few points you will see the pattern of an eclipse