Question:
The equation of the pair of asymptotes of the hyperbola \( 4x^2 - 9y^2 - 24x - 36y - 36 = 0 \) is:
The equation of the pair of asymptotes of the hyperbola \( 4x^2 - 9y^2 - 24x - 36y - 36 = 0 \) is:
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To find the equation of the asymptotes of a hyperbola, eliminate the constant term from its equation.
Updated On: Mar 24, 2025
- \( 2x^2 - xy - 3y^2 - 14x - 9y - 12 = 0 \)
- \( 2x^2 - xy - 3y^2 - 2x + 3y = 0 \)
- \( 2x^2 - 5xy + 3y^2 - 22x + 27y + 60 = 0 \)
- \( 4x^2 - 9y^2 - 24x - 36y = 0 \)
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The Correct Option is D
Solution and Explanation
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: \[ 4x^2 - 9y^2 - 24x - 36y = 0. \]
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: \[ 4x^2 - 9y^2 - 24x - 36y = 0. \]
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