$x - 2 = t^2$ and $y = 2t$ are the parametric equations of which parabola?

One of the points on the parabola $y^2 = 12x$ with focal distance $12$ is:

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

The tangents at the points $A(1, 3)$ and $B(1, -1)$ on the parabola $y^{2} - 2x - 2y = 1$ meet at the point $P$. Then the area (in unit$^{2}$) of the triangle $PAB$ is:

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

If $x = t^2$ and $y = 2t$,then the equation of the normal at $t = 1$ is