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  4. If (2,0) is the vertex and the y-axis is the directrix of a parabola, then its focus is

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Q. If $(2,0)$ is the vertex and the y-axis is the directrix of a parabola, then its focus is

Conic Sections

Solution:

Vertex is $(2,0)$. Since, $y$ -axis is the directrix of a parabola.
$\therefore $ Equation of directrix is $x =0 .$ So, axis of parabola is x-axis. Let the focus be $(a, 0)$
image
Distance of the vertex of a parabola from directrix = its distance from focus
So, $OV = VF \Rightarrow 2= a -2 \Rightarrow $ Focus is $(4,0)$