Question:
The equations of the asymptotes of the hyperbola \( xy + 3x - 2y - 10 = 0 \) are
The equations of the asymptotes of the hyperbola \( xy + 3x - 2y - 10 = 0 \) are
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For \( xy \)-type hyperbola, factorization gives asymptotes directly.
Updated On: May 1, 2026
- \( x=-2, y=-3 \)
- \( x=2, y=-3 \)
- \( x=2, y=3 \)
- \( x=4, y=3 \)
- \( x=3, y=4 \)
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The Correct Option is B
Solution and Explanation
Concept:
Shift origin to remove linear terms.
Step 1: Rearrange equation.
\[ xy + 3x - 2y = 10 \]
Step 2: Add constants to complete factorization.
\[ (x-2)(y+3) = 16 \]
Step 3: Identify center.
\[ (2,-3) \]
Step 4: Asymptotes for rectangular hyperbola.
\[ x-2 = 0,\quad y+3=0 \]
Step 5: Final equations.
\[ x=2,\quad y=-3 \]
Step 1: Rearrange equation.
\[ xy + 3x - 2y = 10 \]
Step 2: Add constants to complete factorization.
\[ (x-2)(y+3) = 16 \]
Step 3: Identify center.
\[ (2,-3) \]
Step 4: Asymptotes for rectangular hyperbola.
\[ x-2 = 0,\quad y+3=0 \]
Step 5: Final equations.
\[ x=2,\quad y=-3 \]
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