Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Total number of lines of the form px + qy+ r = 0 (where pq 
0) that intersect the ellipse 
at two integral points (points whose coordinates are integers) is equal to
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
54
If y 
I then y 
{-7, -6, ...., 0,1,... , 6,7}
Total integral points on 
+ y 2 = 50 are 12 which are
Total number of lines passing through at least two points among these are 12 C 2 = 66 in which
x = 2, x = -2, x = 14, x = -14, x = 10, x = -10, y = 1, y = 7, y = - 1, y= -7, y = 5, y = - 5 are rejected.
Total number of lines are 66 - 12 = 54.
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