Determining the Equation of a Circle

Date: 05/12/2000 at 00:07:47
From: Cody
Subject: Equations on a coordinate plane

Which of the following equations describes the set of all points (x,y) 
in the coordinate plane that are a distance of 5 from the point 
(-3,4)?

     a.  (x+3) + (y-4) = 5
     b.  (x-3) + (y+4) = 5
     c.  (x+3)^2 + (y-4)^2 = 5
     d.  (x+3)^2 + (y-4)^2 = 25
     e.  (x-3)^2 + (y+4)^2 = 25

I think the answer is (a) because none of the other answers work out 
(I think). Is this correct? Why?

Date: 05/12/2000 at 12:00:30
From: Doctor Rob
Subject: Re: Equations on a coordinate plane

Thanks for writing to Ask Dr. Math, Cody.

No, (a) is not the correct answer. Try x = 1000, y = -994, which is 
much farther from (-3,4) than 5 units. Besides, equations of degree 1 
represent lines, which stretch off to infinity.

The set of points described forms a circle with center (-3,4) and 
radius 5. One point on that circle has coordinates (-3-5,4) = (-8,4), 
which is 5 units from (-3,4) in the negative-x direction. Try these 
coordinates in each equation to see which one is satisfied.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/