Description
write an equation for the locus of points in the coordinate plane that are 4 units from (-5 2)
Explanation & Answer
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]
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.Review
Review
24/7 Homework Help
Stuck on a homework question? Our verified tutors can answer all questions, from basic math to advanced rocket science!
Similar Content
Related Tags
To the Lighthouse
by Virginia Woolf
The Road
by Cormac McCarthy
The Call of the Wild
by Jack London
Blink
by Malcolm Gladwell
Dr Jekyll And Mr Hyde
by Robert Louis Stevenson
Epic of Gilgamesh
by Unknown
The President is Missing
by James Patterson, Bill Clinton
No Exit
by Taylor Adams
Twelve Years A Slave
by Solomon Northrup