Eccentricity of the curve ${x^2} - {y^2} = {a^2}$ is
$2$
$\sqrt 2 $
$4$
None of these
(b) Eccentricity of rectangular hyperbola is $\sqrt 2 .$
The length of the transverse axis of a hyperbola is $7$ and it passes through the point $(5, -2)$. The equation of the hyperbola is
At the point of intersection of the rectangular hyperbola $ xy = c^2 $ and the parabola $y^2 = 4ax$ tangents to the rectangular hyperbola and the parabola make an angle $ \theta $ and $ \phi $ respectively with the axis of $X$, then
If area of quadrilateral formed by tangents drawn at ends of latus rectum of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is equal to square of distance between centre and one focus of hyperbola, then $e^3$ is ($e$ is eccentricity of hyperbola)
Eccentricity of conjugate hyperbola of $16x^2 – 9y^2 – 32x – 36y – 164 = 0$ will be-
The coordinates of the foci of the rectangular hyperbola $xy = {c^2}$ are
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