Need math help to write an equation for the locus of points

Mathematics
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write an equation for the locus of points in the coordinate plane that are 4 units from (-5 2)

Dec 29th, 2015

Thank you for the opportunity to help you with your question! I immediately see how to answer the question. This is essentially a "vocabulary" question.

Write an equation for the locus of points that are 4 units from (-5, 2).

This follows immediately from the distance formula:

d = sqrt[(x_1 - x_2)^2 + (y_1 - y_2)^2]

Here d is the distance between points (x_1,y_1) and (x_2,y_2) and sqrt means square root. We are given d = 4, the point (-5,2), and let (x,y) be a point in the locus. Just plug this into the above equation:

4 = sqrt[(x-(-5))^2 + (y- 2)^2]

We are essentially done, but let us now put this in standard form. Square both sides to get rid of sqrt

(x+5)^2 + (y-2)^2 = 16

(As you can see, I also switched the order and used x - (-5) = x + 5.) This is the standard form for the equation of a circle. So the locus is a circle of radius 4 centered at (-5,2). We are done.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 29th, 2015

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