The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is $6$. The equation of the hyperbola referred to its axes as axes of co-ordinates is
$3{x^2} - {y^2} = 3$
${x^2} - 3{y^2} = 3$
$3{x^2} - {y^2} = 9$
${x^2} - 3{y^2} = 9$
The differential equation $\frac{{dx}}{{dy}}= \frac{{3y}}{{2x}}$ represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity :
If $(0,\; \pm 4)$ and $(0,\; \pm 2)$ be the foci and vertices of a hyperbola, then its equation is
The graph of the conic $ x^2 - (y - 1)^2 = 1$ has one tangent line with positive slope that passes through the origin. the point of tangency being $(a, b). $ Then Eccentricity of the conic is
The equation of a tangent to the hyperbola $4x^2 -5y^2 = 20$ parallel to the line $x -y = 2$ is
The eccentricity of the hyperbola conjugate to ${x^2} - 3{y^2} = 2x + 8$ is