Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis
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 is $(0,0)$ and the axis of the parabola is the $x$-axis, the equation of the parabola is either of the form $y^{2}=4 a x$ or $y^{2}=-4 a x$.
The parabola passes through point (2, 3), which lies in the first quadrant.
Therefore, the equation of the parabola is of the form $y^{2}=4 a x$, while point
$(2,3)$ must satisfy the equation $y^{2}=4 a x$.
$\therefore 3^{2}=4 a(2) \Rightarrow a=\frac{9}{8}$
$y^{2}=4\left(\frac{9}{8}\right) x$
$y^{2}=\frac{9}{2} x$
$2 y^{2}=9 x$
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