Question

How many points (X,Y) with integral co ordinates are there whose distance from (1,2)is two units?​

Answer 1

Answer:

4 points

Step-by-step explanation:

They are (1,0)(-1,2)(0,1)(3,2)

Answer 2

Step-by-step explanation:

PQ = 2 => PQ^2 = 4

(x-1)^2 + (y-2)^2 = 4+0 or

= 0+4

possibilities for integral coordinates

⇒(X−1) ^2 + (y−2) ^2 =4+0 or

=0+4

Check (1) (x−1)^ 2 = 4 (y−2) ^2 = 0

⇒x−1=2,−2 ,y−2=0

x=3,−1 ,y=2

(3,2) and (−1,2)

check (2) (x−1) ^2 = 0 , (y−2) ^2 = 4

x=1 , y−2=2, −2

x=1 , y=4, y=0

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(1,4) and (1,0)

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Total 4 integral coordinates are possible

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