solve the following-

1. 

 Let the point b is (6,k)  [B cannot be (-6,k)]

Then, √(3²+(k-4)²≤4

9+(k-4)²≤16

4- √7≤k ≤4+ √7

Hence, the integral solutions are k= 2,3,4,5,6

So, the number of positions of B with integral co-ordinates is 5.

 

2.

Let (h, 0) be such a point.

From the given condition, we have:

(h - 2)² + 3² = c²

h² - 4h + (13 - c²) = 0

Now, h will be real if b² - 4ac ≥0

or, if 16 - 4(13 - c²) ≥0

or, if c² - 9 ≥0

or, if |c| ≥ 3

Hence, there is no point.