$\begin {array} {1 1} (A)\;2x^2=25y & \quad (B)\;2x^2=-25y \\ (C)\;2y^2=25x & \quad (D)\;2y^2=-25x \end {array}$

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- Equation of the parabola along y - axis and opening upwards is $x^2=4ay$
- Equation of the parabola along y - axis and opening downwards is $ x^2=-4ay$

The given vertex is (0,0) and

the parabola is symmetric about the y - axis.

Hence the equation of the parabola is either of the form.

$x^2=4ay $ or $ x^2 = -4ay$

The curve passes through the point (5,2) .

Now substituting for x and y we get,

$(5)^2=-4a(2)$

$ \Rightarrow 25 = -8a$ or

$a = -\large\frac{25}{8}$

Hence the equation of the parabola is

$ x^2=-4 \bigg( \large\frac{25}{8} \bigg)$$y$

(i.e) $x^2=-\large\frac{25}{2}$$y$

or $2x^2=-25y$ is the required equation of the parabola.

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