Question

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

• A. (0,0)
• B. (-2,0)
• C. (4,0)
• D. (-4,0)

Answer 1

Answer: (C)

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 $(a,0)$

Distance of the vertex of a parabola from directrix = its distance from focus
So, $OV=VF\Rightarrow 2=a-2\Rightarrow$ Focus is $(4,0)$