Question 213444
Suppose that a circle has an equation of the form x^2 + y^2 =r^2, r>0. What is the center of the circle? What is the radius of the circle?


Step 1.  Note this is a distance equation using the Pythagorean Theorem.


Step 2.  Note the square of the distance between two points (x,y) and (xc,yc) is:


{{{(x-xc)^2+(y-yc)^2=r^2}}}  where {{{r=sqrt((x-xc)^2+(y-yc)^2)}}} is the distance or radius.


Step 3.  Note that (xc,yc) is the center of a circle.  For this example (xc,yc)=(0,0)


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J