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

Answer 1

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 $y^2=4ax$
$\therefore 3^2=4a\left(2\right)$
$\Rightarrow a=\frac{9}{8}$
Thus, the equation of the parabola is
$y^2=4\left(\frac{9}{8}\right)x$
$y^2=\frac{9}{2}x$
$2y^2=9x$