The standard form of the equation of a circle is
r^2=(x-h)^2 + (y-k)r2=(x−h)2+(y−k),
where hh is the xx-coordinate of the center of the circle, kk is the yy-coordinate of the center of the circle, and rr is the radius of the circle. We will be using this equation to get the answer to the question you have asked, so remember that it is quite important.
The center of the circle that we are asked about in the question is given to be the origin, which is (0,0)(0,0). Therefore, h=0h=0 and k=0k=0. Also, we were given that the radius of the circle is 55, so r=5r=5. Now, let's plug hh , rr, and kk into our standard form of a circle equation:
r^2=(x-h)^2 + (y-k)r2=(x−h)2+(y−k)
(5)^2 = (x-0)^2 + (y-0)^2(5)2=(x−0)2+(y−0)2
Now, let's simplify:
(5)^2 = (x-0)^2 + (y-0)^2(5)2=(x−0)2+(y−0)2
25= x^2 + y^225=x2+y2
color(red)(x^2 + y^2 = 25)x2+y2=25
I hope that helps!
