On a coordinate grid, where is the center of this circle? x2 + y2 = 2

Hello :
 the standard form is: (x-a)²+(y-b)²=r²
 the center is A(a,b)     r ridus
x²+y² =2
(x-0)²+(y-0)² = 2
the center is :O(0,0)

A) Slopes are different, then they must meet at some point, which will be the point of intersection of those two equations.

They can't meet at more than one point, 'cause after that they will propagate in their corresponding directions.

B.) Slopes are same, in such case, lines are parallel, Hence, they won't intersect. They will propagate infinitely in same direction

Hope this helps!