A parabola passes through the points  $(0,1),(-1,3),(3,3)$ and $(2,1)$ has vertex  $(\alpha ,\beta )$ directrix $lx+my+1=0,$  then match the following

Column - I		Column - II
A)	Value of  $\alpha$	P)	0
B)	Value of  $3\beta$	Q)	1
C)	Value of  $l$	R)	4
D)	Sum of digits of m	S)	6
		T)	2

 $A(0,1),B(-1,3),C(3,3),D(2,1)$
Slope of AD = slope of BC = 0
$\therefore$   they are parallel chords
$\therefore$  mid point M (1, 1) & N (1, 3)
  $\therefore$ axis parallel to  $\overleftrightarrow{MN}i.e.,x=1$
$\therefore$   axis parallel to y-axis
$\therefore y=a{x}^2+bx+c$  is parabola
$solving y=\frac{2}{3}{x}^2-\frac{4}{3}x+1$

$Vertex:(1,\frac{1}{3})$

$Directrix y+\frac{1}{24}=0\Rightarrow 24y+1=0$

$\alpha =1;\beta =\frac{1}{3};l=0;m=24$