Question

The straight lines 3x − 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another. The value of a is ______.

Options

• `-5/12`

• `5/12`

• `12/5`

• `-12/5`

Answer 1

The straight lines 3x − 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another. The value of a is `ulbb(12/5)`.

Explanation:

For two lines a₁x + b₁y = c₁ = and a₂x + b₂y = c₂ to be perpendicular, the product of their x coefficients plus the product of their y coefficients must be zero:

(a₁ × a₂) + (b₁ × b₂) = 0

Identify coefficients:

⇒ Line 1 (3x − 5y = 7): a₁ = 3, b₁ = −5

⇒ Line 2 (4x + ay + 9 = 0): a₂ = 4, b₂ = a

Plug into formula:

3(4) + (−5)(a) = 0

12 − 5a = 0

5a = 12

∴ `a = 12/5`