Question

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

Answer 1

_Given that _

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

$y^2= 4 × 3 x$

i.e. $y^2= 12x$ (Ans.)