Let `C` be any circle with centre `(0,sqrt(2))dot` Prove that at most two rational points can be there on `Cdot` (A rational point is a point both of whose coordinates are rational numbers)

Explanation

Equation of any circle with centre at `(0,sqrt(2
)​)` is given by

`(x−0)^2+(y−sqrt(2
)​)^2=r^2`

`x^2+y^2−2sqrt(2)
​=r^2−2 ........ (1)`

where r>0
Let `p(x_1​y_1​),Q(x_2​y_2​)R(x_3​y_3​)` be three destinct rational points on (1) since a straight line meet a circle in at most two point either `y_1or,y_2`
​
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