If the normal to the parabola $y^2 = 4ax$ at the point $(a, 2a)$ meets the parabola again at the point $(at^2, 2at)$,then what is the value of $t$?

The equations of the sides $AB$ and $AC$ of a triangle $ABC$ are $(\lambda+1) x +\lambda y =4$ and $\lambda x +(1-\lambda) y +\lambda=0$ respectively. Its vertex $A$ is on the $y$-axis and its orthocentre is $(1,2)$. The length of the tangent from the point $C$ to the part of the parabola $y^2=6 x$ in the first quadrant is

Find the equation of the latus rectum of the parabola $x^2 = -12y$.

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

$(1, 1)$ is the vertex and $x+y+1=0$ is the directrix of a parabola. If $(a, b)$ is its focus and $(c, d)$ is the point of intersection of the directrix and the axis of the parabola,then $a+b+c+d=$

Let the normal at the point $P$ on the parabola $y^{2} = 6x$ pass through the point $(5, -8)$. If the tangent at $P$ to the parabola intersects its directrix at the point $Q$,then the ordinate of the point $Q$ is