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Find the equation of the parabola that satisfies the given conditions: Vertex (0,0) passing through (2,3) and axis is along x-axis.

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

     Vertex (0,0) passing through (2,3) and axis is along x-axis.

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Given

The Vertex of the parabola is  (0,0).

The parabola is passing through (2,3) and axis is along the x-axis, it will open towards right. and the standard equation of such parabola is 

y^2=4ax

Now since it passes through (2,3) 

3^2=4a(2)

9=8a

a=\frac{8}{9}

So the Equation of Parabola is ;

\Rightarrow y^2=4\left(\frac{9}{8}\right)x

\Rightarrow y^2=\left(\frac{9}{2}\right)x

\Rightarrow 2y^2=9x

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