$\begin {array} {1 1} (A)\;2y^2=9x & \quad (B)\;2y^2=-9x \\ (C)\;2x^2=9y & \quad (D)\;2x^2=-9y \end {array}$

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- Equation of a parabola along the x - axis and opening rightward is $ y^2=4ax$
- Equation of a parabola along the x - axis and opening leftward is $ y^2=-4ax$

The given vertex is (0,0)

It is also given that the axis of the parabola is x - axis.

Hence the equation of the parabola should be of the form $y^2=4ax$ or $y^2=-4ax$

The parabola passes through the point (2, 3)

Now substituing for x and y we get

$(3)^2=4a(2)$

$ \Rightarrow 9 = 8a$

$ \therefore a = \large\frac{9}{8}$

Hence the equation of the parabola is

$y^2=4 \bigg( \large\frac{9}{8} \bigg)$$x$

(i.e) $y^2=\large\frac{9}{2}$$x$

or $2y^2=9x$ is the required equation of the parabola.

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