The length of the common chord of the two circles $x^2+y^2-4 x-8 y+4=0$ and $x^2+y^2-8 x-12 y+16=0$ is

If the focal chord drawn through the point $(1,2)$ to the parabola $y^2=8 x$ meets this parabola in $\left(x_1, y_1\right)$ and $\left(x_2, y_2\right)$, then $x_1+x_2=$

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