General equation of such parabola is
$x=A y^{2}+B y+ C(A \neq 0)$
Since, it passes though $(-2,1),(1,2)$ and $(-1,3)$ therefore, we get
$-2 =A+B+C$ ...(i)
$1 =4 A+2 B+C$ ...(ii)
and $ -1=9 A+3 B+C$ ...(iii)
On subtracting Eq. (i) from Eq. (ii) and Eq. (ii) from Eq. (iii), we get
$3 A+B=3$ ...(iv)
and $5 A+B=-2$ ...(v)
On subtracting Eq. (iv) from Eq. (v), we get
$2 A=-5 \Rightarrow A=-\frac{5}{2}$
From Eq. (iv), we get
$-\frac{15}{2}+B=3$
$\Rightarrow B=3+\frac{15}{2}=\frac{21}{2}$
From Eq. (ii), we get
$\frac{-5}{2}+\frac{21}{2}+C=-2$
$\Rightarrow C+8=-2$
$\Rightarrow C=-10$
Thus, required equation of parabola is
$x=-\frac{5}{2} y^{2}+\frac{21}{2} y-10$
$\Rightarrow 2 x=-5 y^{2}+21 y-20$
$\Rightarrow 5 y^{2}+2 x-21 y+20=0$