2000
Mathematics
67ca00ce0c643c71d77dee1f
A predator moves in a circle of radius √2 centre (0,0), while a prey moves along the line y = x. If 0 ≤ x ≤ 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: (1,1) only
Explanation
x2 + y2 = (√2)2 x2 + y = 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.
x2 + y2 = (√2)2 x2 + y = 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.THIS WEEK's
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