Write the equation in standard form for the circle passing through ( - 6,0) centered at the origin.

The equation for a circle:

          [tex]\boxed { \boxed { (x - a)^2 + (y - b)^2 = r^2}}[/tex]

Since the centre is at (0,0),  then the equation will be:

           [tex]\boxed { \boxed {x^2 + y^2 = r^2}}[/tex]

It passed through (-6, 0) :

           [tex] (-6)^2 + 0^2 = r^2[/tex]

           [tex] r^2 = 6^2[/tex]

           [tex]r = 6[/tex]

The radius is 6, therefore the equation of the circle is :
 
            [tex]x^2 + y^2 = 6^2[/tex]

            [tex]\boxed { \boxed { x^2 + y^2 = 36}}[/tex]