If $\left(2 t^2, 4 t\right)$ is a point on the parabola $y^2=8 x$ such that its focal distance is 3 , then $t=$

The length of the latusrectum of an ellipse is 6 units and the distance between a focus and its nearest vertex on the major-axis is $5 / 3$ units. If $e$ is the eccentricity of this ellipse, then $e$ satisfies the equation

If the line $2 x-3 y+4=0$ cuts the ellipse $x=3 \cos \theta, y=5 \sin \theta$ in $A$ and $B$ and $(\alpha, \beta)$ is the mid-point of $A B$, then $3 \beta-2 \alpha=$

Let $e_1$ be the eccentricity of a hyperbola for which distance between its focii is 2 times the distance between its directrices and $e_2$ be the eccentricity of another hyperbola for which the length of its transverse axis is twice the length of its conjugate axis. Then, $e_1 e_2=$