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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)
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B
(2,0)
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C
(0,2)
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D
(4,0)
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Solution

The correct option is B (2,0)
Focus of the parabola is S(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.
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)

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