A predator moves in a circle of radius \sqrt2 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?
A
(1,1) only
B
(1,1) and (1,2)
C
(0,0) and (1,1)
D
(√2,√2) only
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
x2 + y2 = (\sqrt2)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.
Source: Myschool Past Questions Archive (Record #795)