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

Question:

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

Solution:

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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