Question 318061
Find the center and radius of the circle. {{{(x  - 1)^2 + y2 =  36}}} 

A) (0, 1);  6 
B) ( 1, 0);  36 
C) ( 1, 0);  6 
D) ( -1, 0);  6 
<pre><b>
The standard equation of a circle is 

{{{(x-h)^2}}}{{{"="}}}{{{(y-k)^2}}}{{{"="}}}{{{r^2}}}

whose center is {{{"(h,k)"}}} and whose radius is {{{r}}}.

{{{(x-1)^2}}}{{{"+"}}}{{{y^2}}}{{{"="}}}{{{36}}}

Write {{{y^2}}} as {{{(y-0)^2}}} and {{{36}}} as {{{6^2}}}

{{{(x-1)^2}}}{{{"+"}}}{{{(y-0)^2}}}{{{"="}}}{{{6^2}}}

When you compare that to 

{{{(x-h)^2}}}{{{"="}}}{{{(y-k)^2}}}{{{"="}}}{{{r^2}}}

you see that h=1, k=0, r=6

So the center is (h,k) = (1,0) and the radius is r = 6

This is the graph:

{{{drawing(400,400,-6,8,-7,7, graph(400,400,-6,8,-7,7),
green(line(1,0,5,4.47)),
circle(1,0,6), grid(1) )}}} 
 
Edwin<pre>