Answer :

Given:


Line a2x + ay + 1 = 0 is perpendicular to the line x – ay = 1


To prove:


The line a2x + ay + 1 = 0 is perpendicular to the line x – ay = 1 for all non-zero real values of a.


Concept Used:


Product of slope of perpendicular line is -1.


Explanation:


The given lines are


a2x + ay + 1 = 0 … (1)


x ay = 1 … (2)


Let m1 and m2 be the slopes of the lines (1) and (2).


m1m2 = -


Hence proved, line a2x + ay + 1 = 0 is perpendicular to the line x ay = 1 for all non-zero real values of a.


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