If the lines 3x + by + 5 = 0 and ax - 5y + 7 = 0 are perpendicular to each other, find the relation connecting a and b.
Straight Line Eq
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Question

If the lines 3x + by + 5 = 0 and ax - 5y + 7 = 0 are perpendicular to each other, find the relation connecting a and b.

KnowledgeBoat · Accepted Answer

Given, Lines 3x + by + 5 = 0 and ax - 5y + 7 = 0 are perpendicular to each other. Then the product of their slopes is -1. Converting 3x + by + 5 = 0 in the form y = mx + c. ⇒ by = -3x - 5 ⇒ y = . Comparing with y = mx + c we get, Slope of first line = m₁ = . Converting ax - 5y + 7 = 0 in the form y = mx + c. ⇒ 5y = ax + 7 ⇒ y = . Comparing with y = mx + c we get, Slope of second line = m₂ = . For perpendicular lines, product of their slopes is -1. ∴ m₁.m₂ = -1. Hence, the relation between a and b is given by 3a = 5b.

Mathematics

If the lines 3x + by + 5 = 0 and ax - 5y + 7 = 0 are perpendicular to each other, find the relation connecting a and b.

Straight Line Eq

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