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

$Since\;the\;vertex\;A\;is\;(0,0)\;and\;the\;axis\;of\;the\;parabola\;is\;the\;x-axis\\* Equation\;of\;the\;parabola\;is\;either\;of\;the\;form\;y^2=4ax\;or\;y^2=-4ax\\* The\;parabola\;passes\;through\;point\;(2,3)\;which\;lies\;in\;the\;first\;quadrant\\* Therefore,\;the\;equation\;of\;the\;parabola\;is\;of\;the\;form\;y^2=4ax\\* Point\;(2,3)\;must\;satisfy\;the\;equation\;y^2=4ax\\*\therefore\;3^2=4a(2)\\* \Rightarrow\;a=\frac{9}{8}\\*Thus,\;the\;equation\;of\;the\;parabola\;is \Rightarrow\;y^2=4(\frac{9}{8})x\\*\Rightarrow\;y^2=\frac{9}{2}x\\*$

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