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

Answer 1

The correct option is C

$(1,0)$

Explanation for the correct option:

To find the vertex:

Focus of the parabola is$(0,0)$ 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
So vertex of parabola is $\left(\frac{0+2}{2},\frac{0+0}{2}\right)=\left(1,0\right)$

Hence the correct option is C