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Question

Show that the line a2x+ay+1=0 is perpendicular to the line xay=1 for all non-zero real values of a.


Solution

a2x+ay+1=0

xay=1

Converting these two equations in the form y=mx+c

y=a2ax1a=ax1a

m1=a

Also, y=xa1a

m2=1a

Thus, m1m2=a×1a=1

The two lines are perpendicular as the product of slopes is -1.

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