Question

How many points (x,y) with integral co-ordinates are there whose distance from (1,2) is two units ?

1.one

1. two

2. three

3. four

Answer 1

Correct option: (4) four

Explanation:

(x - 1)2 + (y - 2)2 = 4

It is possible only

Case I

(x - 1)2 = 0 and (y - 2)2 = 4

=> x = 1 and y = 0 , 4

so the points are (1 , 0) , (1 , 4)

Case II

(x - 1)2 = 4 and (y - 2)2 = 0

=> x = 3 , - 1 and y = 2

so the points are (3 , 2) , (3 , - 1)

So total four points are