Question

Find the equation of the parabola that satisfies the following conditions: Vertex $(0,0)$; focus $(3,0)$

Answer 1

Vertex $A(0,0)$ ; focus $S(3,0)$
Since, the vertex of the parabola is $(0,0)$ and the focus lies on the positive $x$-axis , so the axis of the parabola is $x$-axis.
Equation of the parabola is of the form $y^2=4ax$
Since, the focus is $(3,0)$, so $a=3$
Thus, the equation of the parabola is $y^2=12x$