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
Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.