let-A-3-4-and-B-is-a-variable-point-on-the-line-x-6-if-AB-lt-4-then-the-number-of-position-of-B-with-integral-coordinates-is-please-help-

Question Number 98598 by MWSuSon last updated on 15/Jun/20

l e t A = (3, 4) a n d B i s a v a r i a b l e p o i n t

o n t h e l i n e ∣ x ∣= 6 . i f \overset{―}{A B} < 4, t h e n t h e

n u m b e r o f p o s i t i o n o f B w i t h i n t e g r a l

c o o r d i n a t e s i s ?

p l e a s e h e l p!

Commented by bobhans last updated on 15/Jun/20

∣ x ∣ = 6 \Rightarrow {\begin{cases} x = - 6 o r \\ x = 6 \end{cases}

case (1) let B (- 6, y) then \sqrt{{(y - 4)}^{2} + 81} < 4

{(y - 4)}^{2} + 81 < 16 \Rightarrow y = \emptyset

case (2) let B (6, y) then \sqrt{{(y - 4)}^{2} + 9} < 4

{(y - 4)}^{2} - 7 < 0 \Rightarrow (y - 4 - \sqrt{7}) (y - 4 + \sqrt{7}) < 0

4 - \sqrt{7} < y < 4 + \sqrt{7}

1.354 < y < 6.64

so position of B with integral coordinates

where y \in {2, 3, 4, 5, 6}

Commented by MWSuSon last updated on 15/Jun/20

Thanks a lot.