Question

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

• A. $5$
• B. $6$
• C. $10$
• D. $12$

Answer 1

The correct option is A $5$

$\left|x\right|=6\therefore x=6orx=-6$

B general point = (6,y)

$\therefore (6-3{)}^2+(y-4{)}^2\le 4^2{y}^2-8y+16\le 4^2-3^2{y}^2-8y+9\le 0(y-(4+\sqrt{7}\left)\right)(y-(4-\sqrt{7}\left)\right)\le 0\therefore Theintegralsolutionsare2,3,4,5,6\therefore 5solutions.$