What is the conjugate hyperbola of the hyperbolax2a2-y2b2-1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Conjugate Hyperbola

What is the c...

Question

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

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

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

Q. Conjugate of the hyperbola,

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

is .

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

Match the following.

$\begin{matrix} Column 1 & Column 2 1. a^{2} > b^{2} & P.Director circle is real 2. a^{2} = b^{2} & Q.Director circle is imaginary 3. a^{2} < b^{2} & R.Centre is the only point from which two perpendicular tangents can be drawn on the hyperbola \end{matrix}$

Q. If the angle between the asymptotes of hyperbola

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

\frac{π}{3} .

Then the eccentricity of conjugate hyperbola is

Join BYJU'S Learning Program

What is the conjugate hyperbola of the hyperbola x2a2−y2b2=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 x2a2−y2b2=1, the equation of conjugate hyperbola is given by x2a2−y2b2=−1

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