Describe continuity of this function

Question

f(x)= x^2/(x^2-y). for (x,y) not equal to (0,0)

0 for (x,y) equal to (0,0)

1. Please show that f(x,y) is not continuous at (0,0)
2. For what other (x,y) is f(x,y) not continuous> why?

Can someone explain this question geometrically and analytically?

Answer 1

1. It is not continuous at (0,0) because the denominator is 0 at that point.

2. It is not continuous anywhere the denominator is 0. In this case, that occurs when y=x^2