Find maximum number of points having integer coordinates (both x, y integer) which can lie on a circle with centre at 
is (are)
Text Solution
Verified by Experts1
(1)Let equation of circle is (x – 
) 2 + (y – 
) = r 2 , (x 1 , y 1 ) & (x 2 , y 2 ) are integer points on circle
(x – 
) 2 + (y – 
) = r 2 , (x 1 , y 1 ) & (x 2 , y 2 )
(x 1 – 
) 2 + (y 1 – 
) 2 = (x 2 – 
) 2 + (y 2 – 
) 2 = r 2
(x 2 – x 1 ) (x 2 + x 1 – 2 
) + (y 2 – y 1 ) (y 2 + y 1 – 2 
) = 0
(x 22 – x 12 ) + (y 22 – y 12 ) = 2 
(y 2 – y 1 ) + 2 
(x 2 – x 1 )
A = 
B + 
C
Therefore A = B = C = 0
x 1 = x 2 & y 1 = y 2
So, no distinct points are possible.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems