A predator moves in a circle of radius √2 centre (0,0), while a prey moves...

JAMB 2000

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

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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.

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