Question

The equation of the pair of asymptotes of the hyperbola \( 4x^2 - 9y^2 - 24x - 36y - 36 = 0 \) is:

• A. \( 2x^2 - xy - 3y^2 - 14x - 9y - 12 = 0 \)
• B. \( 2x^2 - xy - 3y^2 - 2x + 3y = 0 \)
• C. \( 2x^2 - 5xy + 3y^2 - 22x + 27y + 60 = 0 \)
• D. \( 4x^2 - 9y^2 - 24x - 36y = 0 \)

Hint:

To find the equation of the asymptotes of a hyperbola, eliminate the constant term from its equation.

Answer 1

The Correct Option is D

The given equation of the hyperbola is: \[ 4x^2 - 9y^2 - 24x - 36y - 36 = 0. \] Step 1: Convert the equation into standard form
Rearranging the equation: \[ 4x^2 - 9y^2 - 24x - 36y = 36. \] For the equation of the asymptotes, we remove the constant term: \[ 4x^2 - 9y^2 - 24x - 36y = 0. \] Step 2: Conclusion
Thus, the equation of the pair of asymptotes is: \[ 4x^2 - 9y^2 - 24x - 36y = 0. \]