If the angle between the tangents drawn to the parabola $y^2=4 x$ from the points on the line $4 x-y=0$ is $\frac{\pi}{3}$, then the sum of the abscissae of all such points is

The normal at a point on the parabola $y^2=4 x$ passes through a point $P$. Two more normals to this parabola also pass through $P$. If the centroid of the triangle formed by the feet of these three normals is $G(2,0)$, then the abscissa of $P$ is

A normal chord $P Q$ drawn at a point $P$ on the parabola $y^2=5 x$ subtends a right angle at the vertex. If $P$ lies in the first quadrant, then the other end $Q$ of the normal chord is

If $L(p, q), q>3$ is one end of the latus rectum of the parabola $(y-2)^2=3(x-1)$, then the equation of the tangent at $L$ to this parabola is