Question

Find all points with integer coordinates that are a distance of square root of 29 from (-4,3)

how do u do this?????!?!?!?!

Answer 1

(x+4)^2 + (y-3)^2 = 29

So 29 has to be sum of two squares.
29 = 25 + 4
Those are the only two integers.

so ..
Case 1: (x+4)^2 = 25 and (y-3)^2 = 4
or
Case 2: (x+4)^2 = 4 and (y-3)^2 = 25

Case 1:
then x + 4 = ±2 and y-3 =±5
x = -2, y = 8
x = -6, y = 8
x = -2 , y = -2
x = -6 , y = -2

Case 1:
x+4 =±5 and y-3 = ±2

x = -1 , y = 5
x = -1 , y = 1
x = -9 , y = 5
x = -9 , y = 1

Case 2:
then x + 4 = ±2 and y-3 =±5

x = -2, y = 8
x = -6, y = 8
x = -2 , y = -2
x = -6 , y = -2

So it looks like 8 points.

Answer 2

(x+4)^2 + (y-3)^2 = 29

So 29 has to be sum of two squares.
29 = 25 + 4
Those are the only two integers.

so ..
Case 1: (x+4)^2 = 25 and (y-3)^2 = 4
or
Case 2: (x+4)^2 = 4 and (y-3)^2 = 25


Case 1:
x+4 =±5 and y-3 = ±2

x = 1 , y = 5
x = 1 , y = 1
x = -9 , y = 5
x = -9 , y = 1

Case 2:
then x + 4 = ±2 and y-3 =±5

x = -2, y = 8
x = -6, y = 8
x = -2 , y = -2
x = -6 , y = -2

So it looks like 8 points.