Question

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

• A. $(0,1)$
• B. $(2,0)$
• C. $(0,2)$
• D. $(1,0)$

Answer 1

Answer: (D)

$(1,0)$

Focus of the parabola is $S\equiv (0,0)$ and $x=2$ is the directrix
And we know that axis of the parabola is perpendicular to the directrix
and pass through the focus of the parabola
Thus foot of directrix is $(2,0)$
Also we know that, vertex of the parabola is the mid point of its focus and the foot of directrix
Hence required vertex is $(1,0)$