Question:
Which of the following is INCORRECT for the hyperbola \( x^2 - 2y^2 + 2x + 8y - 1 = 0 \)?
Which of the following is INCORRECT for the hyperbola \( x^2 - 2y^2 + 2x + 8y - 1 = 0 \)?
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To find the lengths of axes for a hyperbola, rewrite the equation in standard form and identify key terms.
Updated On: Jan 12, 2026
- Its eccentricity is \( \sqrt{2} \)
- Its equation is \( x^2 - 2y^2 + 2x + 8y - 1 = 0 \)
- Length of the transverse axis is \( 2\sqrt{3} \)
- Length of the conjugate axis is \( 2\sqrt{6} \)
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The Correct Option is D
Solution and Explanation
Step 1: Use the standard equation of hyperbola.
By converting the given equation into the standard form of a hyperbola and comparing terms, we calculate the length of the axes. The conjugate axis length is incorrect as stated in option (D).
Step 2: Conclusion.
The correct answer is (D).
By converting the given equation into the standard form of a hyperbola and comparing terms, we calculate the length of the axes. The conjugate axis length is incorrect as stated in option (D).
Step 2: Conclusion.
The correct answer is (D).
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