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?
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(1,1) only
- (1,1) and (1,2)
- (0,0) and (1,1)
- (√2,√2) only
The correct answer is: A
Explanation
x2 + y2 = (√2)2x2 + 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.
There is an explanation video available .