How do you write the equation for a circle with center of circle (-3,0) radius with endpoint (3,0)?

1 Answer
Aug 27, 2017

Answer:

#(x+3)^2 + y^2 = 36#

Explanation:

The equation of a circle is #(x-h)^2 + (y-k)^2 = r^2#, where #(h,k)# is the center and #r# is the radius.

If the center is at #(-3,0)# and the endpoint of the radius is at #(3,0)#, then the length of the radius is the distance between the two points, which is #3-(-3) = 6#.

We can substitute #color(blue)((color(blue)(-3, 0))# for #(h,k)#, and #color(red)6# for #r#.

#(x-h)^2 + (y-k)^2 = r^2#

#(x- color(blue)((-3)))^2 + (y-color(blue)0)^2 = color(red)6^2#

#(x+3)^2 + y^2 = 36#

We can check this by graphing. The center of the circle is at #(-3,0)# and the endpoint of the radius is at #(3,0)#, so our equation is correct.

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