$P$ and $Q$ are two distinct points on the parabola,$y^2 = 4x$,with parameters $t$ and $t_1$ respectively. If the normal at $P$ passes through $Q$,then the minimum value of $t_1^2$ is

If $a$ and $c$ are the segments of a focal chord of a parabola and $b$ is the semi-latus rectum,then:

If two perpendicular rays from the focus of the parabolic surface $y^2 = 4x$ are incident at points $A(t_1^2, 2t_1)$ and $B(t_2^2, 2t_2)$ such that $t_1t_2 = -1$,then the distance between the reflected rays is -

If the line $3x - 2y + 12 = 0$ intersects the parabola $4y = 3x^2$ at the points $A$ and $B$,then at the vertex of the parabola,the line segment $AB$ subtends an angle equal to

$PQ$ is any focal chord of the parabola $y^2=32x$. The length of $PQ$ can never be less than: ............ $unit$

Let the equation of the tangent at a point $P$ on the parabola $x^2-4x-4y+16=0$ be $2x-y-5=0$. If the equation of the normal drawn at $P$ to this parabola is $ax+y+c=0$,then find the value of $ac$.