solve the following-

Asked by Hritwik Kashyap | 27th Nov, 2013, 10:19: PM

Expert Answer:

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.

Answered by  | 28th Nov, 2013, 10:53: PM

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