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Find the equation of the parabola that satisfies the given conditions: Vertex (0,0), passing through (5,2) and symmetric with respect to y-axis.

12.  Find the equation of the parabola that satisfies the given conditions:

       Vertex (0,0), passing through (5,2) and symmetric with respect to y-axis.

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Given a parabola,

with Vertex (0,0), passing through (5,2) and symmetric with respect to the y-axis.

Since the parabola is symmetric with respect to Y=axis, it's axis will ve Y-axis. and since it passes through the point (5,2), it must go through the first quadrant.

So the standard equation of such parabola is 

x^2=4ay

Now since this parabola is passing through (5,2)

5^2=4a(2)

25=8a

a=\frac{25}{8}

Hence the equation of the parabola is 

\Rightarrow x^2=4\left ( \frac{25}{8} \right )y

\Rightarrow x^2=\left ( \frac{25}{2} \right )y

\Rightarrow 2x^2=25y

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