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  4. A parabola has the origin as its focus and the line x=2 as the directrix. Then the vertex of the parabola is at

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Q. A parabola has the origin as its focus and the line $x=2$ as the directrix. Then the vertex of the parabola is at

Conic Sections

Solution:

Vertex of a parabola is the mid-point of focus and the point
image
where directrix meets the axis of the parabola.
Here focus is $O(0,0)$ and directxix meets the axis at $B(2,0)$
$\therefore $ Vertex of the parabola is $(1,0)$