Question

Conjugate of the hyperbola, $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is .

• A. x2a2+yb2=1
• B. x2a2-y2b2=1
• C. x2a2-y2b2=-1
• D. -x2a2-y2b2=1

Answer 1

The correct option is C x2a2-y2b2=-1

We say hyperbola A is the conjugate hyperbola of the hyperbola B, if the transverse axis of A is the conjugate axis of the hyperbola B and vice versa. For the standard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, the equation of conjugate hyperbola is given by $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$