Question

The equations of the parabola whose axis is parallel to the $X$ - axis and which passes through the points $(-2,1),(1,2)(-1,3)$ is

• A. $18y^2-12x-21y-21=0$
• B. $5y^2+2x-21y+20=0$
• C. $15y^2+12x-11y+20=0$
• D. $25y^2-2x-65y+36=0$

Answer 1

Answer: (B)

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