Length of Chord

Q. If the $x$-intercept of the focal chord of the parabola $y^2-2y-4x+5=0$ is $\frac{11}{4}$, then find the length of chord.

1. $\frac{15}{2}$
2. $\frac{25}{2}$
3. $\frac{25}{4}$
4. $\frac{15}{4}$

Q. Let $P\left(t_1\right),Q\left(t_2\right)$ be two points on the parabola $y^2=8x.$ Then which of the following is/are true?

1. If the chord $PQ$ meets the $x-$axis at $(4,0)$, then $t_1{t}_2=-2$
2. If $PQ$ is a focal chord, then $t_1{t}_2=-2$
3. If $t_1=2$, then the length of focal chord $PQ$ is $\frac{25}{4}$
4. If $t_1=-\frac{1}{2}$ and $PQ$ meets the $x-$axis at $(4,0)$, then $Q\equiv (32,16)$

Q. $y^2=4x$ and $y^2=-8(x-a)$ intersect at point $A$ and $C$. Points $O(0,0),A,B(a,0),C$ are concyclic.
Tangents to parabola $y^2=4x$ at $A$ and $C$ intersect at point $D$ and tangents to parabola $y^2=-8(x-a)$ intersect at point $E$, then the area of quadrilateral $DAEC$ is

1. $96\sqrt{2}$
2. $48\sqrt{3}$
3. $54\sqrt{5}$
4. $36\sqrt{6}$