Question

What is the conjugate hyperbola of the hyperbola
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

• A. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
• B. $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
• C. $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$
• D. $-\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

Answer 1

The correct option is C

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$

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
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$