Question

Equation of the parabola whose axis is parallel to $Y-axis$ and which passes through the point $(1,0)$, $(0,0)$ and $(-2,4)$

• A. ${2x}^2+2x=3y$
• B. ${2x}^2-2x=3y$
• C. ${2x}^2+2x=y$
• D. ${2x}^2-2x=y$

Answer 1

The correct option is B ${2x}^2-2x=3y$

$\because$Axis of the parabola is parallel to $Y-axis$

$\therefore$ General equation of the parabola is

$y=A{x}^2+Bx+c$

$\Rightarrow a=A+B+C$ ($\because (1,0)$ lies on the parabola)

$\Rightarrow A+B+C=0\_\_\_\_\_\_\_\_\left(1\right)$

Similarly for $(0,0)$

$\Rightarrow 0=0+6+c\Rightarrow c=0\Rightarrow A+B=0\_\_\_\left(2\right)$ from equation $\left(1\right)$

and

$4=A{(-2)}^2+B(-2)+0$

$\Rightarrow 4A-2B=4\Rightarrow 2A-B=2$

$\Rightarrow 3A=2\Rightarrow A=\frac{2}{3},B=\frac{-2}{3}$

$\therefore y=\frac{2}{3}{x}^2-\frac{2}{3}x\Rightarrow 2x^2-2x=3y$