From a point $(d, 0)$, three normals are drawn to the parabola $y^{2} = x$. Then:

If tangent lines are drawn from the point $(-1, 2)$ to the parabola $y^2 = 4x$, then the area of the triangle (in sq. units) formed by the chord of contact and the tangents drawn is: (in $\sqrt{2}$)

The equation of the parabola whose focus is $(5, 3)$ and directrix is $3x - 4y + 1 = 0$ is:

The equation of the normal to the parabola $y^{2} = x + a$ with slope $m$ is .....

The maximum possible area bounded by the parabola $y=x^2+x+10$ and a chord of the parabola of length $1$ is

If $(2 t^2, 4 t)$ is a point on the parabola $y^2 = 8x$ such that its focal distance is $3$,then $t =$