The number of rational point(s) (a point ( a , b ) is rational, if a and b both are rational numbers) on the circumference of a circle having centre π , e is

Step-by-step solution

Let two points ( x 1 , y 1 ) and ( x 2 , y 2 ) lie on the circumference of a circle with centre π , e where x 1 , y 1 , x 2 , y 2 ∈ Q Point x , y equidistant from x 1 , y 1 & ( x 2 , y 2 ) will lie on the perpendicular bisector of this line segment. y - y 1 + y 2 2 = - x 2 - x 1 y 2 - y 1 x - x 1 + x 2 2 ⇒ p x + q y + r = 0 where p , q , r ∈Q Now it must pass through π , e ⇒ p π + q e + r = 0 ⇒ p = q = r = 0 There is no such line possible, hence atmost one point lies on the circle.