The combined equation of the asymptotes of the hyperbola 2x² + 5xy + 2y² + 4x + 5y = 0 is -

Correct Answer is : 2x22x²2x2 + 5xy + 2y22y²2y2 + 4x + 5y + 2 = 0

2x² + 5xy + 2y² + 4x + 5y + 2 = 0

2x² + 5xy + 2y² + 4x + 5y - 2 = 0

Correct Answer is : 2x22x²2x2 + 5xy + 2y22y²2y2 + 4x + 5y + 2 = 0

Test Index

VITEEE 2018 Paper

Section: Mathematics

Question : 111 of 125

Marks: +1, -0

2x^2

2y^2

Solution:

Let the equation of asymptotes be

2x^2

+ 5xy +

2y^2

+ 4x + 5y + λ = 0.......(1)

This equation represents a pair of straight lines,

.∴ abc + 2fgh -

af^2

bg^2

ch^2

= 0

∴ 4λ + 25 -

\frac{25}{2}

- 8 - λ ×

\frac{25}{4}

= 0

⇒ -

\frac{9\lambda}{4} + \frac{9}{2}

= 0 ⇒ λ = 2

Putting the value of A, in eq. (1),

we get

2x^2

+ 5 xy +

2y^2

+ 4x + 5y + 2 = 0

this is the equation of the asymptotes.

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