Question

The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is 6. The equation of the hyperbola referred to its axes as axes of coordinates are:

• A. \( 3x^2 - y^2 = 3 \)
• B. \( x^2 - 3y^2 = 3 \)
• C. \( 3x^2 - y^2 = 9 \)
• D. \( x^2 - 3y^2 = 9 \)

Hint:

For hyperbolas, use the relationship \( c^2 = a^2 + b^2 \) to find the parameters of the equation and apply known conditions like conjugate axis length.

Answer 1

The Correct Option is C