Conic-Sections Question 553
Question: The number of points (a, b) where a and b are positive integers lying on the hyperbola $ x^{2}-y^{2}=512 $ is
Options:
A) 3
B) 4
C) 5
D) 6
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ a^{2}-b^{2}=512\Rightarrow (a+b)(a-b)=2^{9} $
$ \Rightarrow (a+b,a-b)=(2^{8},2),(2^{7},2^{2}),(2^{6},2^{3}),(2^{5},2^{4}) $ Since $ a>b,a+b>a-b $ therefore the other combinations like $ (2^{4},2^{5}) $ etc. cannot be accepted $ (2^{9},1) $ also cannot be accepted since a and b are positive integers.
BETA
