The equations of the parabola whose axis is parallel to the $X$-axis and which passes through the points…

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
  1. $18 y^2-12 x-21 y-21=0$
  2. $5 y^2+2 x-21 y+20=0$
  3. $15 y^2+12 x-11 y+20=0$
  4. $25 y^2-2 x-65 y+36=0$

Solution

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} $

Asked in: AP EAMCET 2017 (26 Apr Shift 1)

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