# Find the equation of the parabola that satisfies the given conditions: Vertex $(0,0)$ and Focus $(3,0)$

$\begin{array}{1 1} y^2=12 x \\ x^2=-12y \\ y^2=-12x \\ x^2=12y \end{array}$

Given Vertex $(0,0)$ and Focus $(3,0)$
Since the vertex is the origin and the focus lies on the positive x-axis, $\rightarrow$ x-axis is the axis of the parabola.
The parabola is of the form $y^2=4ax$.
Since Focus = $(3,0) \rightarrow a = 3$
Therefore the equation of the parabola is $y^2 = 4 \times 3x = 12x$