The eccentricity of the hyperbola $2{x^2} - {y^2} = 6$ is
$\sqrt 2 $
$2$
$3$
$\sqrt 3 $
Length of latusrectum of curve $xy = 7x + 5y$ is
The eccentricity of curve ${x^2} - {y^2} = 1$ is
If the foci of the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{{b^2}}} = 1$ coincide with the foci of the hyperbola $\frac{{{x^2}}}{{144}} - \frac{{{y^2}}}{{81}} = \frac{1}{{25}},$ then $b^2$ is equal to
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 line $3x - 4y = 5$ is a tangent to the hyperbola ${x^2} - 4{y^2} = 5$. The point of contact is