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# Find the equation of a parabola that satisfies the following condition - Vertex $(0,0)$ and passing through $(2,3)$ and axis is x-axis.

$\begin{array}{1 1} y^2 = \large\frac{9}{2} x \\ y^2 = \large\frac{9}{4} x \\y^2 = -\large\frac{9}{2} x \\ y^2 = -\frac{9}{4} x\end{array}$

Given vertex is origin and axis is x-axis, the equation is of the form $y^2 = 4ax$ of $y^2 = -4ax$.
Since the parabola passes through $(2,3)$, the equation is of the form $y^2=4ax$ which means that $3^2 = 4 \times a \times 2 \rightarrow a = \large\frac{9}{8}$
Therefore, the equation of the parabola is $y^2 =4 \large\frac{9}{8}$$x = \large\frac{9}{2}$$ x$
edited Apr 1, 2014