Question

Prove that the equation 2x2+xy-6y2+7y-2=0
represents a pair of straight lines.​

Answer 1

Step-by-step explanation:

(2*x2)+xy+(7*y)-(6*y2)==2

Answer 2

Given:

The given equation is $2x^2 + xy - 6y^2 + 7y - 2 =0$

To prove:

The given equation represents a pair of straight lines.

Solution:

To prove that the given equation represents a pair of straight-line we will firstly compare it with the general equation of the straight line.

General equation of straight line = $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$

Comparing this with the given equation we have,

a = 2, h = 0.5, b = -6, g = 0, f = 3.5, c = -2

Now to prove that the given equation represents a pair of straight-line we have to prove

Δ = $abc + 2fgh - af^2 - bg^2 - ch^2 = 0$

= $2(-6)(-2) + 2(3.5)(0.5)(0) - 2(3.5)^2 - (-6)(0)^2 - (-2)(0.5)^2$

= 24 - 24.5 + 0.5

= 0

Therefore, The given equation represents a pair of straight lines.