The reciprocal of the eccentricity of rectangular hyperbola, is

The foci of the hyperbola $2{x^2} - 3{y^2} = 5$, is

The equation of the hyperbola whose foci are $(6, 4)$ and $(-4, 4)$ and eccentricity $2$ is given by

Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellips $x^2+4 y^2=4$. If the hyperbola passes through a focus of the ellipse, then

$(A)$ the equation of the hyperbola is $\frac{x^2}{3}-\frac{y^2}{2}=1$

$(B)$ a focus of the hyperbola is $(2,0)$

$(C)$ the eccentricity of the hyperbola is $\sqrt{\frac{5}{3}}$

$(D)$ the equation of the hyperbola is $x^2-3 y^2=3$

The normal to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1$ at the point $(8,3 \sqrt{3})$ on it passes through the point

The equation of the tangents to the conic $3{x^2} - {y^2} = 3$ perpendicular to the line $x + 3y = 2$ is