A rectangular hyperbola of latus rectum $2$ units passes through $(0, 0)$ and has $(1, 0)$ as its one focus. The other focus lies on the curve -
$4x^2 + y^2 = 1$
$x^2 + y^2 = 9$
$x^2 -y^2 = 1$
$4x^2 -y^2 = 1$
The equation of a tangent to the hyperbola $4x^2 -5y^2 = 20$ parallel to the line $x -y = 2$ is
The equation of the hyperbola in the standard form (with transverse axis along the $x$ - axis) having the length of the latus rectum = $9$ units and eccentricity = $5/4$ is
The line $lx + my + n = 0$ will be a tangent to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, if
The distance between the directrices of a rectangular hyperbola is $10$ units, then distance between its foci is
The equation of common tangents to the parabola ${y^2} = 8x$ and hyperbola $3{x^2} - {y^2} = 3$, is