Q5 of 112 Page 166

Find the value of a if the straight lines 5x – 2y – 9 = 0 and ay + 2x – 11 = 0 are perpendicular to each other.

Given: The straight lines 5x – 2y – 9 = 0 and ay + 2x – 11 = 0 are perpendicular to each other.


As the lines are perpendicular to each other, the product of their slopes is equal to –1.


Slope of the first line 5x – 2y – 9 = 0 is m1.


()


Slope of the second line ay + 2x –11 = 0 is m2.



Therefore,


⇒


As the lines are perpendicular m1× m2 = –1


⇒


⇒ a = 5


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