If the line $2 x+3 y+n=0$ is a tangent to the parabola $y^2=8 x$, then the equation of the normal drawn at the point $(2 n, 4 \sqrt{n})$ to the parabola $y^2=8 x$ is

$a x-y+c=0$ is the equation of the common tangent to the parabola $y^2=8 \sqrt{5} x$ and the circle $x^2+y^2=1$. If this tangent makes an acute angle with the positive $X$-axis in the positive direction, then $a^2 c^2=$

If the focal distance of a point $P\left(2, y_1\right)$ on the parabola $y^2=k x$ is 3 , then the equation of the tangent drawn at $P$ to the given parabola is

Normals are drawn from the point $P(8,0)$ to the parabola $y^2=12 x$. If $\theta$ is the acute angle between two non-horizontal normals among them, then $\tan \theta=$