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If a = (3,4) and B is a variable point on the lines |x| = 6. If AB ≤ 4 , then the no. of positions of B with integral coordinates is :-
(a) 5 (b) 6 (c) 10 (d) 12
|x| = 6
x can be 6 or -6
let point be B = { (6,y) or (-6,y) }
AB can be
AB = [(6-3)2 + (y-4)2]1/2 or [(-6-3)2+(y-4)2]1/2
AB ≤ 4 so
9 + (y-4)2 ≤ 16 or 81 + (y-4)2 ≤ 16
(y-4)2 - (root7)2 ≤0 or ( minimum value of (y-4)2 =0, enequality does not holds good)
only possible solution is
(y-4)2-(root7) 2 ≤ 0
(y-(4+root7)) (y-(4-root7)) ≤ 0
for this enequality , 4-root7 ≤ y ≤ 4 + root7
1.36 ≤ y ≤ 6.64
y can take value 2 , 3, 4, 5, 6
total solutions for y are 5 , total number of points should be 5...
so option a is correct...
approve if u like my ans
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