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Question

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


A

(2,0)

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B

(0,2)

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C

(1,0)

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D

(0,1)

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Solution

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=2is 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 0+22,0+02=1,0

Hence the correct option is C


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