Question

A parabola has the origin as its focus and the line $x=4$ as the directrix. Then the vertex of the parabola is at

• A. $(0,4)$
• B. $(2,0)$
• C. $(0,2)$
• D. $(4,0)$

Answer 1

The correct option is B $(2,0)$

Focus of the parabola is $S\equiv (0,0)$
and $x=4$ is the directrix.
we know that axis of the parabola is perpendicular to the directrix and pass through the focus of the parabola.
$\therefore$ intersection of directrix and axis of the parabola is $(4,0)$
Also, vertex of parabola is the mid point of its focus and foot of directrix.
Hence, required vertex $=(2,0)$