The number of rational points on the circle 
(X-√2)^2+(y-√3)^2=k(K€R) is atmost.........
(Rational points are points whose both 
co ordinates are rational)

Asked by Sunil Soni | 22nd Sep, 2015, 10:08: AM

Expert Answer:

open parentheses x minus square root of 2 close parentheses squared plus open parentheses y minus square root of 3 close parentheses squared equals K space i s space a space c i r c l e space w i t h space c e n t r e space left parenthesis square root of 2 comma space square root of 3 right parenthesis space a n d space r a d i u s space square root of K. W h e r e space K space i s space a space r a t i o n a l space n u m b e r comma space w h i c h space i s space p o s s i b l e space i f b o t h space open parentheses x minus square root of 2 close parentheses squared space a n d space open parentheses y minus square root of 3 close parentheses squared space a r e space r a t i o n a l. space open parentheses x minus square root of 2 close parentheses squared space i s space r a t i o n a l space i f space x equals a square root of 2 comma space w h e r e space a element of Z. open parentheses y minus square root of 3 close parentheses squared space i s space r a t i o n a l space i f space y equals b square root of 3 comma space w h e r e space b element of Z. x equals a square root of 2 space i s space r a t i o n a l space o n l y space i f space a equals 0. space H e n c e comma space x equals 0. y equals b square root of 3 space i s space r a t i o n a l space o n l y space i f space b equals 0. space H e n c e comma space y equals 0. H e n c e comma space t h e space o n l y space r a t i o n a l space p o i n t space left parenthesis x comma space y right parenthesis space w h i c h space w i l l space s a t i s f y t h e space e q u a t i o n space i s space left parenthesis 0 comma space 0 right parenthesis. H e n c e comma space a t m o s t space O N E space s u c h space p o i n t space i s space p o s s i b l e.

Answered by satyajit samal | 22nd Sep, 2015, 11:01: AM