Question

Which of the following is INCORRECT for the hyperbola \( x^2 - 2y^2 + 2x + 8y - 1 = 0 \)?

• A. Its eccentricity is \( \sqrt{2} \)
• B. Its equation is \( x^2 - 2y^2 + 2x + 8y - 1 = 0 \)
• C. Length of the transverse axis is \( 2\sqrt{3} \)
• D. Length of the conjugate axis is \( 2\sqrt{6} \)

Hint:

To find the lengths of axes for a hyperbola, rewrite the equation in standard form and identify key terms.

Answer 1

The Correct Option is D

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).