Question

The combined equation of the asymptotes of the hyperbola \[ 2x^2 + 5xy + 2y^2 + 4x + 5y = 0 \] is:

• A. \( 2x^2 + 5xy + 2y^2 + 4x + 5y + 2 = 0 \)
• B. \( 2x^2 + 5xy + 2y^2 + 4x + 5y - 2 = 0 \)
• C. \( 2x^2 + 5xy + 2y^2 = 0 \)
• D. None of these

Hint:

To find the asymptotes of a hyperbola, remove the constant terms from the equation and solve the quadratic equation.

Answer 1

The Correct Option is C

Step 1: The asymptotes of the hyperbola are found by solving the corresponding quadratic equation.
Step 2: The combined equation of the asymptotes is \( 2x^2 + 5xy + 2y^2 = 0 \).

Final Answer: \[ \boxed{2x^2 + 5xy + 2y^2 = 0} \]