Question

If $A(3,4)$ and $B$ is a variable point on the lines $|x|=6$. If $AB\le 4$ then number of positions of $B$ with integral co-ordinates is:

• A. $5$
• B. $4$
• C. $6$
• D. $10$

Answer 1

The correct option is A $5$

$AB\le 4$
$\Rightarrow \sqrt{{(3\pm 6)}^2+{(y-4)}^2}\le 4$
$\Rightarrow {(y-4)}^2\le 7$
or ${(y-4)}^2\le -65$ ....{ which is not possible }
$\Rightarrow 4-\sqrt{7}\le y\le 4+\sqrt{7}$
Therefore, possible integers for $y$ are $2,3,4,5,6.$

Ans: A