A predator moves in a circle of radius √2 centre (0,0), while a prey moves along the line y = x. If 0 $\leq$ x $\leq$ 2, at which point(s) will they meet?

(1,1) only

(1,1) and (1,2)

(0,0) and (1,1)

(√2,√2) only

Correct answer is A

x² + y² = (√2)²
x² + y² = 2
but y = x

Thus; x² + x² = 2
2x² = 2
x² = + or - 1

But x² + y² = 2
1² + y² = 2
1 + y² = 2
y² = 2 - 1
y² = 1
y = + or - 1

Thus point (x,y) = (1,1) only.

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