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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

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

Grade:12

1 Answers

vikas askiitian expert
509 Points
11 years ago

|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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