What is the graph of (x – 1)^2 + (y – 3)^2 = 4 ?

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Question

What is the graph of (x – 1)^2 + (y – 3)^2 = 4 ?

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chihiroasleaf · Answer

$$(x-a)^{2}+(y-b)^{2}=r ^{2}$$
is the equation of circle with centre at (a,b) and its radius is r,

from the equation, what is the centre of the circle? and what is the radius? :)

anonymous · Answer

When I pull out a and b wouldn't they change to positive right?

chihiroasleaf · Answer

yes.., 
so, what is the centre of the circle?

anonymous · Answer

(1,3)

chihiroasleaf · Answer

correct... :D

and what is the radius of the circle then?

anonymous · Answer

Uh... 4

chihiroasleaf · Answer

hhmm.., the equation of circle is 
$$(x-a)^{2}+(y-b)^{2}=r ^{2}$$
with the radius is r,
so the right-hand side is the square of the radius..

anonymous · Answer

2 then right?

chihiroasleaf · Answer

yess..., :D

so, the circle is a circle with radius 2 and the centre at (1,3)
so, which one is your graph? :)

anonymous · Answer

Both choice 1 and 3 have a center (1,3) but I'm not sure how to tell the radius.

chihiroasleaf · Answer

what do you know about the radius of a circle?

anonymous · Answer

Oh isn't that like half of the diameter

chihiroasleaf · Answer

correct.... :D

anonymous · Answer

I got it, thanks again! I have an essay question I could use help on if you're available!

chihiroasleaf · Answer

you're very welcome... :)