Let 
be non-zero complex numbers and 
be the set of solutions 
of the equation 
, where 
. Then, which of the following statement(s) is (are) TRUE? (JEE Advanced 2018)
has exactly one element, then 
, then L has infinitely many elements 
is at most 2 
has more than one element, then 
has infinitely many elements
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a, c, d)
Given 
… .. (i)
Taking conjugate, we get
………… (ii)
Adding (i) and (ii), we get
Clearly, this is the equation of a straight line.
Now, eliminating 
from (i) and (ii), we get
If 
, then 
has unique solution.
If 
and 
, then 
has infinite solutions.
If 
and 
, then 
has no solution.
Thus, 
has either unique, infinite or no solution.
Also, line can intersect circle in maximum two points.
So, number of elements in 
is at most 2.
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