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/
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