Question

If the slope of one of the Jines represented by ax² + (2a + 1)xy + 2y² = 0 be reciprocal of the slope of the other, then the slope of the lines are ______.

Options

• `3/2, 2/3`

• `(-1)/2, -2`

• `1/3, 3`

• `(-1)/3, -3`

Answer 1

If the slope of one of the Jines represented by ax² + (2a + 1)xy + 2y² = 0 be reciprocal of the slope of the other, then the slope of the lines are `(-1)/2, -2`.

Explanation:

Given equation of pair of lines is ax² + (2a + 1 )xy + 2y² = 0 

∴ A = a, H = `(2"a" + 1)/2`, B = 2

According to the given condition,

m₁ = `1/"m"_2`

⇒ m₁m₂ = 1

Now, m₁m₂ = `"a"/2`

⇒ `"a"/2` = 1

⇒ a = 2

Also, m₁ + m₂ = `- ((2"a" + 1)/2) = (-5)/2`

⇒ `"m"_1 + 1/"m"_1 = (-5)/2`

⇒ `2"m"_1^2 + 5"m"_1 + 2` = 0

∴ m₁ = `(-1)/2` or –2