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?
-
A.
(1,1) only -
B.
(1,1) and (1,2) -
C.
(0,0) and (1,1) -
D.
(√2,√2) only
Correct Answer: Option A
Explanation
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.