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Question

Find the value of a if the straight lines 5x2y9=0 and ay+2x11=0 are perpendicular to each other.

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Solution

Consider the straight lines 5x2y9=0 and ay+2x11=0

Given the lines are perpendicular, m1×m2=1

Consider 5x2y9=0

2y=5x9

y=52x92

Slope m1=52

Consider ay+2x11=0

ay=2x+11

y=2a+11a

Slope m2=2a

We have m1×m2=1

52×2a=1

5a=1

a=5

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