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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
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Verified Answer
The correct answer is:
$5 y^2+2 x-21 y+20=0$
Let, general equation of this parabola
$$
x=A y^2+B y+C
$$
It is given that, it passes through the points $(-2,1),(1,2)$ and $(-1,3)$ so, we get
On solving Eqs. (i), (ii) and (iii), we get
$$
A=\frac{-5}{2}, B=\frac{21}{2} \text { and } C=-10
$$
Hence, equation of parabola
$$
\begin{aligned}
& x=-\frac{5}{2} y^2+\frac{21}{2} y-10 \\
\Rightarrow \quad & 2 x=-5 y^2+21 y-20 \\
\Rightarrow \quad & 5 y^2+2 x-21 y+20=0
\end{aligned}
$$
$$
x=A y^2+B y+C
$$
It is given that, it passes through the points $(-2,1),(1,2)$ and $(-1,3)$ so, we get
On solving Eqs. (i), (ii) and (iii), we get
$$
A=\frac{-5}{2}, B=\frac{21}{2} \text { and } C=-10
$$
Hence, equation of parabola
$$
\begin{aligned}
& x=-\frac{5}{2} y^2+\frac{21}{2} y-10 \\
\Rightarrow \quad & 2 x=-5 y^2+21 y-20 \\
\Rightarrow \quad & 5 y^2+2 x-21 y+20=0
\end{aligned}
$$
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