Question

If the equation `lambdax^2 + 2y^2 - 5xy + 5x - 7y + 3 = 0` represents two straight lines, then the value of λ will be ______.

Options

• 3

• 2

• 8

• – 8

Answer 1

If the equation `lambdax^2 + 2y^2 - 5xy + 5x - 7y + 3 = 0` represents two straight lines, then the value of λ will be 2.

Explanation:

The given equation represents two straight lines.

∴ abc + ²fgh – af – bg² – ch² = 0

⇒ `lambda(2)(3) + 2((-7)/2) (5/2) ((-5)/2) - lambda((-7)/2)^7 - 2(5/2)^2 - 3((-5)/2)^2` = 0

⇒ `6lambda + 175/4 - 49/4 lambda - 25/2 - 75/4` = 0

⇒ 25λ = 50

⇒ λ = 2